LIBRARY 

rS  '     f.  "',,    "' 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 


Class 


WORKS  OF 
PROFESSOR   CECIL   H.   PEABODY 

PUBLISHED   BY 

JOHN   WILEY   &    SONS. 


Thermodynamics  of  the  Steam-engine  and  other 
Heat-engines. 

This  work  is  intended  for  the  use  of  students  in 
technical  schools,  and  gives  the  theoretical  training 
required  by  engineers.  Sixth  Edition,  Revised,  vii 
-f  543  pages,  119  figures.  8vo,  cloth,  $5.00. 

Table*   of    the    Properties    of    Steam    and    other 
Vapors,   and  Temperature-Entropy  Table. 

These  tables  were  prepared  for  the  use  of  students 
in  technical  schools  and  colleges,  and  of  engineers  in 
general.  Eighth  Edition,  Rewritten.  8vo,  vi  +  133 
pages,  cloth,  $1.00. 

Valve-dears  for  Steam-engines. 

This  book  is  intended  to  give  engineering  students 
instruction  in  the  theory  and  practice  of  designing 
valve-gears  for  steam-engines.  Second  Edition, 
Revised  and  Enlarged.  8vo,  v  +  142  pages,  33  fold- 
ing-plates, cloth,  $2.50. 

Steam-boilers. 

By  Prof.  Cecil  H.  Peabody  and  Prof.  Edward  F. 
Miller.  Nearly  400  pages ;  142  illustrations.  8vo, 
cloth,  $4.00. 

Manual  of  the  Steam-engine  Indicator. 

154  pages  ;  98  figures.    12mo,  cloth,  $1.50. 
Naval  Architecture. 

v  +  616  pages  ;  217  figures.    8vo,  cloth,  $7.50. 


THERMODYNAMICS 


OF  THE 


STEAM-ENGINE 

AND 

OTHER    HEAT-ENGINES 


BY 

CECIL    H.  PEABODY 

PROFESSOR    OF    NAVAL   ARCHITECTURE   AND   MARINE    ENGINEERING, 
MASSACHUSETTS   INSTITUTE   OF  TECHNOLOGY 


SIXTH  EDITION,    REVISED 
TOTAL   ISSUE,  ELEVEN   THOUSAND 


NEW    YORK 

JOHN   WILEY   &   SONS 

LONDON:  CHAPMAN  &   HALL,  LIMITED 

1909 


GENERAL 


COPYRIGHT,  1889,  1898,  1907,  1909 

BY 
CECIL  H.  PEABODY 


PREFACE  TO  SIXTH   EDITION. 


WHEN  this  work  was  first  in  preparation  the  author  had  before 
him  the  problem  of  teaching  thermodynamics  so  that  students  in 
engineering  could  use  the  results  immediately  in  connection  with 
experiments  in  the  Engineering  Laboratories  of  the  Massachu- 
setts Institute  of  Technology.  The  acceptance  of  the  book  by 
teachers  of  engineering  appears  to  justify  the  general  plan,  which 
will  be  adhered  to  now  that  the  development  of  engineering  and 
presentation  of  new  physical  investigations  call  for  a  complete 
revision. 

The  author  is  still  of  the  opinion  that  the  general  mathematical 
presentation  due  to  Clausius  and  Kelvin  is  the  most  satisfactory, 
and  carries  with  it  the  ability  to  read  current  thermodynamic 
investigation  by  physicists  and  engineers.  At  the  same  time  it  is 
recognized  that  recent  determinations  of  the  properties  of  both 
saturated  and  superheated  steam  so  far  narrow  the  applications  of 
the  general  method  that  there  is  justification  for  those  who  prefer 
special  methods  for  those  applications.  To  provide  for  both 
views  of  this  subject,  the  general  mathematical  discussion  is  pre- 
sented in  a  separate  chapter,  which  may  be  omitted  at  the  first 
reading  (or  altogether),  provided  that  the  special  methods  which 
are  also  given  in  the  proper  places  are  taken  to  be  sufficient. 

Following  the  method  of  the  first  edition  the  original  experi- 
mental data,  on  which  the  working  equations  whether  logical  or 
empirical  must  be  based,  are  given  with  particularity,  to  afford 
an  idea  of  the  degree  of  precision  to  be  attributed  to  calculations 
made  by  their  aid.  The  properties  of  perfect  gases  and  of 
both  saturated  and  superheated  steam  are  now  determined  with  a 
satisfactory  degree  of  certainty  and  precision,  so  that  the  physical 

iii 


196478 


iv  PREFACE 

constants  and  the  tables  required  by  engineers  can  be  used  with 
confidence,  and  may  be  expected  to  have  permanence.  The 
author's  "Tables  of  the  Properties  of  Steam,  etc.,"  were  originally 
computed  to  accompany  the  first  edition  of  the  work;  this  present 
edition  is  accompanied  by  a  new  edition  of  the  "Steam  and 
Entropy  Tables"  which  have  been  entirely  recomputed  from  new 
and  precise  experimental  data.  The  temperature-entropy  table  will 
be  found  to  give  ready  and  exact  solutions  of  all  adiabatic  prob- 
lems for  both  saturated  and  superheated  steam,  and  of  many 
other  problems.  It  allows  of  the  use  of  certain  rapid  and  refined 
computations  for  steam  turbines  which  cannot  be  so  readily 
determined  without  it. 

There  is  presented  in  this  book,  firstly,  a  presentation  of  the 
fundamental  conceptions  and  processes  of  thermodynamics;  sec- 
ondly, a  statement  of  the  properties  and  characteristics  of  gases  and 
of  vapors,  and  their  treatment  by  thermodynamic  methods  so  as  to 
provide  solutions  of  problems  that  arise  in  engineering;  thirdly,  a 
discussion  of  steam-engines,  internal  combustion  engines,  air-com- 
pressors, refrigerating  machines,  injectors  and  steam-turbines.  As" 
far  as  possible  the  work  is  so  arranged  that  any  individual  discussion 
may  be  read  by  itself  in  any  order.  Discretion  can,  therefore,  be 
used  in  teaching,  and  in  reading  or  rereading  the  several  sub- 
jects discussed. 

A  feature  which  has  been  given  prominence  in  the  first  and 
in  all  subsequent  editions  is  the  presentation  of  the  results  of 
tests  on  steam  engines  and  other  machines,  with  the  idea  of 
qualifying  the  student  to  comprehend  the  significance  of  such 
results,  and  to  judge  for  himself  the  performance  to  be  expected 
from  engines  and  machines  under  test  and  in  practice.  Adequate 
laboratory  experience,  such  as  is  now  given  in  all  well-equipped 
engineering  schools,  is  essential  for  the  proper  conception  of  this 
side  of  the  subject;  and  conversely,  an  adequate  theoretical  train- 
ing, such  as  this  book  aims  to  give,  is  essential  for  efficient  labora- 
tory instruction. 

Whenever  direct  quotations  have  been  made,  references  have 
been  given  in  footnotes.  It  does  not  appear  necessary  to  add 


PREFACE  V 

other  acknowledgments  of  assistance  from  well-known  authors, 
further  than  to  say  that  their  writings  have  been  diligently 
searched  in  the  preparation  of  this  book,  since  any  text-book 
must  be  largely  an  adaptation  of  their  work  to  the  needs  of 
instruction. 

C.  H.  P. 
JUNE,  1909. 


TABLE  OF  CONTENTS. 


I.   THERMAL  CAPACITIES i 

II.   FIRST  LAW  or  THERMODYNAMICS 13 

III.  SECOND  LAW  OF  THERMODYNAMICS  „ 22 

IV.  GENERAL  THERMODYNAMIC  METHOD  ; 43 

V.   PERFECT  GASES 54 

VI.   SATURATED  VAPOR 76 

VII.   SUPERHEATED  VAPORS ....  100 

VIII,   THE  STEAM-ENGINE 128 

IX.   COMPOUND  ENGINES 156 

X.  TESTING  STEAM-ENGINES     183 

XL  INFLUENCE  OF  THE  CYLINDER  WALLS 199 

XII.   ECONOMY  OF  STEAM-ENGINES 237 

XIII.  FRICTION  OF  ENGINES 285 

XIV.  INTERNAL-COMBUSTION  ENGINES 298 

XV.   COMPRESSED  AIR 358 

XVI.  REFRIGERATING  MACHINES 396 

XVII.   FLOW  OF  FLUIDS 423 

XVIII.   INJECTORS    ... .    .    '. 447 

XIX.   STEAM-TURBINES t   .   .   .   .   .  472 


OF    THE 

UNIVERSITY 

OF 


THERMODYNAMICS  OF  THE  STEAM-ENGINE. 


CHAPTER    I. 

THERMAL  CAPACITIES, 

THE  object  of.  thermodynamics,  or  the  mechanical  theory  of. 
heat,  is  the  solution  of.  problems  involving  the  action  of  heat, 
and,  for  the  engineer,  more  especially  those  problems  presented 
by  the  steam-engine  and  other  thermal  motors.  The  substances 
in  which  the  engineer  has  the  most  interest  are  gases  and  vapors, 
more  especially  air  and  steam.  Fortunately  an  adequate  treat- 
ment can  be  given  oi  these  substances  for  engineering  purposes. 

First  General  Principle.  —  In  the  development  of  the  theory 
of  thermodynamics  it  is  assumed  that  if  any  two  characteristics 
or  properties  of  a  substance  are  known  these  two,  treated  as 
independent  variables,  will  enable  us  to  calculate  any  third 
property. 

As  an  example,  we  have  from  the  combination  of  the  laws  of 
Boyle  and  Gay-Lussac  the  general  equation  for  gases, 

pv  =  RT, 

in  which  p  is  the  pressure,  v  is  the  volume,  T  is  the  absolute 
temperature  by  the  air-thermometer,  and  R  is  a  constant  which 
for  air  has  the  value  53.35  when  English  units  are  used.  It  is 
probable  that  this  equation  led  to  the  general  assumption  just 
quoted.  That  assumption  is  purely  arbitrary,  and  is  to  be  justi- 
fied by  its  results.  It  may  properly  be  considered  to  be  the  first 
general  principle  of  the  theory  of  thermodynamics;  the  other 
two  general  principles  are  the  so-called  first  and  second  laws  of 
thermodynamics,  which  will  be  stated  and  discussed  later. 


2  THERMAL   CAPACITIES 

Characteristic  Equation.  —  An  equation  which  gives  the 
relations  of  the  properties  of  any  substance  is  called  the  charac- 
teristic equation  for  that  substance.  The  properties  appearing 
in  a  characteristic  equation  are  commonly  pressure,  volume, 
and  temperature,  but  other  properties  may  be  used  if  convenient. 
The  form  of  the  equation  must  be  determined  from  experiments, 
either  directly  or  indirectly. 

The  characteristic  equation  for  a  gas  is,  as  already  quoted, 

pv  =  RT. 

The  characteristic  equation  for  an  imperfect  gas,  like  super- 
heated steam,  is  likely  to  be  more  complex;  for  example,  the 
equation  given  by  Knoblauch,  Linde,  and  Klebe  is 


On  the  other  hand,  the  properties  of  saturated  steam,  especially 
if  mixed  with  water,  cannot  be  represented  by  a  single  equation. 

Specific  Pressure.  —  The  pressure  is  assumed  to  be  a  hydro- 
static pressure,  such  as  a  fluid  exerts  on  the  sides  of  the  con- 
taining vessel  or  on  an  immersed  body.  The  pressure  is 
consequently  the  pressure  exerted  by  the  substance  under  con- 
sideration rather  than  the  pressure  on  that  substance.  For 
example,  in  the  cylinder  of  a  steam-engine  the  pressure  of  the 
steam  is  exerted  on  the  piston  during  the  forward  stroke  and 
does  work  on  the  piston;  during  the  return  stroke,  when  the 
steam  is  expelled  from  the  cylinder,  it  still  exerts  pressure  on 
the  piston  and  abstracts  work  from  it. 

For  the  purposes  of  the  general  theory  pressures  are 
expressed  in  terms  of  pounds  on  the  square  foot  for  the  English 
system  of  units.  In  the  metric  system  the  pressure  is  expressed 
in  terms  of  kilograms  on  the  square  metre.  A  pressure  thus 
expressed  is  called  the  specific  pressure.  In  engineering  practice 
other  terms  are  used,  such  as  pounds  on  the  square  inch,  inches 
of  mercury,  millimetres  of  mercury,  atmospheres,  or  kilograms 
on  the  square  centimetre. 


TEMPERATURE  3 

Specific  Volume.  —  It  is  convenient  to  deal  with  one  unit  of 
weight  of  the  substance  under  discussion,  and  to  consider  the 
volume  occupied  by  one  pound  or  one  kilogram  of  the  substance ; 
this  is  called  the  specific  volume,  and  is  expressed  in  cubic  feet  or 
in  cubic  metres.  The  specific  volume  of  air  at  freezing-point 
and  under  the  normal  atmospheric  pressur^  is  12.39  cubic  feet; 
the  specific  volume  of  saturated  steam  at  2i2°F.  is  26.6  cubic 

feet;  and  the  specific  volume  of  water  is  about •,  or  nearly 

62.4 

o.o 1 6  of  a  cubic  foot. 

Temperature  is  commonly  measured  by  aid  of  a  mercurial 
thermometer  which  has  for  its  reference-points  the  freezing- 
point  and  boiling-point  of  water.  A  centigrade  thermometer 
has  the  volume  of  the  stem  between  the  reference- points  divided 
into  one  hundred  equal  parts  called  degrees.  The  Fahrenheit 
thermometer  differs  from  the  centigrade  in  having  one  hundred 
and  eighty  degrees  between  the  freezing-point  and  the  boiling- 
point,  and  in  having  its  zero  thirty-two  degrees  below  freezing. 

The  scale  of  a  mercurial  thermometer  is  entirely  arbitrary, 
and  its  indications  depend  on  the  relative  expansion  of  glass  and 
mercury.  Indications  of  such  thermometers,  however  carefully 
made,  differ  appreciably,  mainly  on  account  of  the  varying 
nature  of  the  glass.  For  refined  investigations  thermometric 
readings  are  reduced  to  the  air-thermometer,  which  has  the 
advantage  that  the  expansion  of  air  is  so  large  compared  with 
the  expansion  of  glass  that  the  latter  has  little  or  no  effect. 

It  is  convenient  in  making  calculations  of  the  properties  of 
air  to  refer  temperatures  to  the  absolute  zero  of  the  scale  of  the 
air-thermometer.  To  get  a  conception  of  what  is  meant  by  this 
expression  we  may  imagine  the  air-thermometer  to  be  made  of 
a  uniform  glass  tube  with  a  proper  index  to  show  the  volume 
of  the  air.  The  position  of  the  index  may  be  marked  at  boiling- 
point  and  at  freezing-point  as  on  the  mercurial  thermometer, 
and  the  space  between  may  be  divided  into  one  hundred  parts 
or  degrees.  If  the  graduations  are  continued  to  the  closed  end 
of  the  tube  there  will  be  found  to  be  273  of  them.  It  will  be 


4  THERMAL   CAPACITIES 

shown  later  that  there  is  reason  to  suppose  that  the  absolute 
zero  of  temperature  is  273°  centigrade  below  the  freezing-point 
of  water.  Speculations  as  to  the  meaning  of  absolute  zero  and 
discussions  concerning  the  nature  of  substances  at  that  temper- 
ature are  not  now  profitable.  It  is  sufficient  to  know  that 
equations  are  simplified  and  calculations  are  facilitated  by  this 
device.  For  example,  if  temperature  is  reckoned  from  the 
arbitrary  zero  of  the  centigrade  thermometer,  then  the  charac- 
teristic equation  for  a  perfect  gas  becomes 


in  which  a  is  the  coefficient  of  dilatation  and  —  =  273  nearly. 

In  order  to  distinguish  the  absolute  temperature  from  the 
temperature  by  the  thermometer  we  shall  designate  the  former 
by  T  and  the  latter  by  /,  bearing  in  mind  that 

T  =  t  +  273°  centigrade, 
T  =  t  +  459.5  Fahrenheit. 

Physicists  give  great  weight  to  the  discussion  of  a  scale  of 
temperature  that  can  be  connected  with  the  fundamental  units 
of  length  and  weight  like  the  foot  and  the  pound.  Such  a  scale, 
since  it  does  not  depend  on  the  properties  of  any  substance 
(glass,  mercury,  or  air),  is  considered  to  be  the  absolute  scale  of 
temperature.  The  differences  between  such  a  scale  and  the 
scale  of  the  air-thermometer  are  very  small,  and  are  difficult  to 
determine,  and  for  the  engineer  are  of  little .  moment.  At  the 
proper  place  the  conception  of  the  absolute  scale  can  be  easily 
stated. 

Graphical  Representation  of  the  Characteristic  Equation.  — 
Any  equation  with  three  variables  may  be  represented  by  a 
geometrical  surface  referred  to  co-ordinate  axes,  of  which  surface 
the  variables  are  the  co-ordinates.  In  the  case  of  a  perfect  gas 
which  conforms  to  the  equation 

pv  =  RT, 


STANDARD   TEMPERATURE 


FlG 


the  surface  is  such  that  each  section  perpendicular  to  the  axis 
of  T  is  a  rectangular  hyperbola  (Fig.  i). 

Returning  now  to  the  general  case, 
it  is  apparent  that  the  characteristic 
equation  of  any  substance  may  be  repre- 
sented  by  a  geometrical  surface  referred 
to  co-ordinate  axes,  since  the  equation  is  ' 
assumed  to  contain  only  three  variables; 
but  the  surface  will  in  general  be  less 
simple  in  form  than  that  representing  the 
combined  laws  of  Boyle  and  Gay-Lussac. 

If  one  of  the  variables,  as  T,  is  given  a  special  constant  value, 
it  is  equivalent  to  taking  a  section  perpendicular  to  the  axis  of 
T\  and  a  plane  curve  will  be  cut  from  the  surface,  which  may 
be  conveniently  projected  on  the  (p,  v)  plane.  The  reason  for 
choosing  the  (p,  v)  plane  is  that  the  curves  correspond  with 
those  drawn  by  the  steam-engine  indicator. 

Considerable  use  is  made  of  such  thermal  curves  in  explaining 
thermodynamic  conceptions.  As  a  rule,  a  graphical  process 
or  representation  is  merely  another  way  of  presenting  an  idea 
that  has  been,  or  may  be,  presented  analytically;  there  is,  how- 
ever, an  advantage  in  representing  a  condition  or  a  change  to 
the  eye  by  a  diagram,  especially  in  a  discussion  which  appears 
to  be  abstract.  A  number  of  thermal  curves  are  explained  on 
page  16. 

Standard  Temperature.  —  For  many  purposes  it  is  convenient 
to  take  the  freezing-point  of  water  for  the  standard  temperature, 
since  it  is  one  of  the  reference-  points  on  the  thermometric  scale; 
this  is  especially  true  for  air.  But  the  properties  of  water  change 
rapidly  at  and  near  freezing-point  and  are  very  imperfectly 
known.  It  has  consequently  become  customary  to  take  62°F. 
for  the  standard  temperature  for  the  English  system  of  units; 
there  is  a  convenience  in  this,  inasmuch  as  the  pound  and  yard 
are  standards  at  that  temperature.  For  the  metric  system  15°  C. 
is  used,  though  the  kilogram  and  metre  are  standards  at  freezing- 
point. 


0  THERMAL  CAPACITIES 

Thermal  Unit.  —  Heat  is  measured  in  calories  or  in  British 
thermal  units  (B.  T.  u.).  A  British  thermal  unit  is  the  heat 
required  to  raise  one  pound  of  water  from  62°  F.  to  63°  F.;  in 
like  manner  a  calorie  is  the  heat  required  to  raise  one  kilogram 
of  water  from  15°  C.  to  16°  C. 

Specific  Heat  is  the  number  of  thermal  units  required  to  raise 
a  unit  of  weight  of  a  given  substance  one  degree  of  temperature. 
The  specific  heat  of  water  at  the  standard  temperature  is,  of 
course,  unity. 

If  the  specific  heat  of  a  given  substance  is  constant^  then  the 
heat  required  to  raise  one  pound  through  a  given  range  of  tem- 
perature is  the  product  of  the  specific  heat  by  the  increase  of 
temperature.  Thus  if  c  is  the  specific  heat  and  t  —  tt  is  the  range 
of  temperature  the  heat  required  is 


If  the  specific  heat  varies  the  amount  of  heat  must  be  obtained 
by  integration  —  that  is, 


Q  =  fcdt, 


and  conversely 

c-®-. 

'  dt 

It  is  customary  to  distinguish  two  specific  heats  for  perfect 
gases;  specific  heat  at  constant  pressure  and  specific  heat  at 
constant  volume,  which  may  be  represented  by 


the  subscript  attached  to  the  parenthesis  indicates  the  property 
which  is  constant  during  the  change.  It  is  evident  that  the 
specific  heats  just  expressed  are  partial  differential  coefficients. 

Latent  Heat  of  Expansion  is  the  amount  of  heat  required  to 
increase  the  volume  of  a  unit  of  weight  of  the  substance  by  one 


EFFECTS   PRODUCED    BY   HEAT 


cubic  foot,  or  one  cubic  metre,  at  constant  temperature.     It 
may  be  represented  by 


Thermal  Capacities.  —  The  two  specific  heats  and  the  latent 
heat  of  expansion  are  known  as  thermal  capacities.  It  is  cus- 
tomary to  use  three  other  properties  suggested  by  those  just 
named  which  are  represented  as  follows: 

/8Q\  (SQ\ 

m  =  (a  J   ;  n  =  (~xl)  and  ° 
V  op/t  \  Sp/v 

The  first  represents  the  amount  of  heat  that  must  be  applied 
to  one  pound  of  a  substance  (such  as  air)  to  increase  the  pressure 
by  the  amount  of  one  pound  per  square  foot  at  constant  tem- 
perature; this  property  is  usually  negative  and  represents  the 
heat  that  must  be  abstracted  to  prevent  the  temperature  from 
rising.  The  other  two  can  be  defined  in  like  manner  if  desired, 
but  it  is  not  very  important  to  state  the  definitions  nor  to  try  to 
gain  a  conception  as  to  what  they  mean,  as  it  is  easy  to  express 
them  in  terms  of  the  first  three,  for  which  the  conceptions  are 
not  difficult.  They  have  no  names  assigned  to  them,  which  is, 
on  the  whole,  fortunate,  as,  of  the  first  three,  two  have  names  that 
have  no  real  significance,  and  the  third  is  a  misnomer. 

General  Equations  of  the  Effects  Produced  by  Heat.  —  In 
order  to  be  able  to  compute  the  amount  of  heat  required  to 
produce  a  change  in  a  substance  by  aid  of  the  characteristic 
equation,  it  is  necessary  to  admit  that  there  is  a  functional  rela- 
tion between  the  heat  applied  and  some  two  of  the  properties 
that  enter  into  the  characteristic  equation.  It  will  appear  later 
in  connection  with  the  discussion  of  the  first  law  of  thermody- 
namics that  an  integral  equation  cannot  in  general  be  written 
directly,  but  we  may  write  a  differential  equation  in  one  of  the 
three  following  forms: 


THERMAL   CAPACITIES 


or  substituting  for  the  partial  differential  coefficients  the  letters 
which  have  been  selected  to  represent  them, 

dQ  =  cvdt  +  Idv       (0 

dQ  =  cpdt  +  mdp (2) 

dQ  =  ndp  +  odv       (3) 

This  matter  may  perhaps  be 
clearer  if  it  is  presented  graph- 
ically as  in  Fig.  2,  where  ab  is 
intended  to  represent  the  path 
of  a  point  on  the  characteristic 
surface  in  consequence  of  the 
addition  of  the  heat  dQ.  There 
will  in  general  be  a  change  of 
temperature  volume  and  pres- 
sure as  indicated  on  the  figure. 
Now  the  path  ab,  which 
for  a  small  change  may 
be  considered  to  be  a  straight 
line,  will  be  projected  on 

the  three  planes  at  a'b',  a"Vf  and  a'"bf".  The  projection  on  the 
(v,T)  plane  may  be  resolved  into  the  components  &v  and  &T-, 
the  first  represents  a  c  .range  of  volume  at  constant  temperature 
requiring  the  heat  Idv,  and  the  second  represents  a  change  of  tem- 
perature at  constant  volume  requiring  the  heat  cpdL  Conse- 
quently the  heat  required  for  the  change  in  terms  of  the  volume 
and  temperature  is 


FIG.  a. 


dQ  =  cvdt  -t-  idv. 


RELATIONS    OF   THE    THERMAL    CAPACITIES  9 

Relations  of  the  Thermal  Capacities.  —  The  three  equations 
(i),  (2),  and  (3),  show  the  changes  produced  by  the  addition  of 
an  amount  of  heat  dQ  to  a  unit  of  weight  of  a  substance,  the 
difference  coming  from  the  methods  of  analyzing  the  changes. 
We  may  conveniently  find  the  relations  of  the  several  thermal 
capacities  by  the  method  of  undetermined  coefficients.  Thus 
equating  the  right-hand  members  of  equations  (i)  and  (2), 

cvdt  +  Idv  =  cpdt  +  mdp      .....     (4) 
From  the  characteristic  equation  we  shall  have  in  general 

v  =  F(p,  T), 
as,  for  example,  for  air  we  have 

RT 

,-T, 

and  consequently  we  may  write 


which  substituted  in  equation  (4)  gives, 

(r\  55 

•£-#  +  jjrdP 

t  +  ldp.     .     (5) 


It  will  be  noted  that,  as  T  differs  from  t  only  by  the  addition 
of  a  constant,  the  differential  dt  may  be  used  in  all  cases,  whether 
we  are  dealing  with  absolute  temperatures,  or  temperatures  on 
the  ordinary  thermometer. 

In  equation  (5)  p  and  T  are  independent  variables,  and  each 
may  have  all  possible  values;  consequently  we  may  equate  like 
coefficients. 

.'.  c,=  c.  +  l  .     ,     .     .    .     .     (6) 


10  THERMAL   CAPACITIES 

Also,  equating  the  remaining  coefficients, 


If  the  characteristic  equation  is  solved  for  the  pressure  we 
shall  have 

p  =  F,  (T,  v), 
so  that 


which  substituted  in  equation  (4)  gives 


cpdt  +  m    --  dt  +  - 


.*.   K,  +  m  ~-  )  dt  +  m  /-dv  =  cvdt  +  Idv. 
\  ol  /  ov 

Equating  like  coefficients, 


Bp 

~  ==  Cv 


From  equations  (2)  and  (3) 

cpdt  +  mdp  =  ndp  -f  odv         .     .     .     .  (n) 

and  from  an  equation 

T  =  F,  (v,  #) 


which  latter  substituted  in  equation  (n)  gives 
f  ,  -  Jv  +  ^   —  dp  +  mdp  =  ndp 


Equating  coefficients  of  </v, 

•  -  V  .......    (12) 


RELATIONS    OF   THE   THERMAL  CAPACITIES  n 

Finally,  from  equations   (i)  and   (3), 

cvdt  +  Idv  =  ndp  +  odv     .....  (13) 

Substituting  for  dt  as  above, 

cv  T—  dv  +  cv  -z—  dp  +  Idv  =  ndp  +  odv. 

Equating  coefficients  of  dp, 


For  convenience  the  several  relations  of  the  thermal  capacities 
may  be  assembled  as  follows  : 

.  dl  ,  St 


&  & 

c  c  " 


to 


They  are  the  necessary  algebraic  relations  of  the  literal  func- 
tions growing  out  of  the  first  general  principle,  and  are  inde- 
pendent of  the  scale  of  temperature,  or  of  any  other  theoretical 
or  experimental  principle  of  thermodynamics  other  than  the  one 
already  stated  —  namely,  that  any  two  properties  of  a  given 
substance,  treated  as  independent  variables,  are  sufficient  to 
allow  us  to  calculate  any  third  property. 

Of  the  six  thermal  capacities  the  specific  heat  at  constant 
pressure  is  the  only  one  that  is  commonly  known  by  direct 
experiment.  For  perfect  gases  this  thermal  capacity  is  a  con- 
stant, and,  further,  the  ratio  of  the  specific  heats 

C-*=K 
Cv 

is  a  constant,  so  that  cv  is  readily  calculated.     The  relations  of 
the   thermal   capacities   allow   us    to    calculate   values   for   the 


12  THERMAL   CAPACITIES 

other  thermal  capacities,  /,  m,  w,  and  0,  provided  that  we  can 
first  determine  the  several  partial  differential  coefficients  which 
appear  in  the  proper  equations.  But  for  a  perfect  gas  the 
characteristic  equation  is 

pv  =  RT, 
from  which  we  have 

*L       R.     *L       £• 

&  ==  JJ      8/  ==  v  ' 

A       H  .     JH   3£ 
8p  ==  R'     bv   '"  R  ' 

Substituting  these  values  in  the  equations  for  the  thermal 
capacities,  we  have 


by  aid  of  which  the  several  thermal  capacities  may  be  calculated 
numerically,  or,  what  is  the  usual  procedure,  may  be  represented 
in  terms  of  the  specific  heats. 


CHAPTER  II. 

FIRST  LAW   OF   THERMODYNAMICS. 

THE  formal  statement  of  the  first  law  of  thermodynamics  is: 

Heat  and  mechanical  energy  are  mutually  convertible,  and 
heat  requires  for  its  production  and  produces  by  its  disappearance 
a  definite  number  of  units  of  work  for  each  thermal  unit. 

This  law,  which  may  be  considered  to  be  the  second  general 
principle  of  thermodynamics,  is  the  statement  of  a  well-deter- 
mined physical  fact.  It  is  a  special  statement  of  the  general 
law  of  the  conservation  of  energy,  i.e.,  that  energy  may  be  trans- 
formed from  one  form  to  another,  but  can  neither  be  created 
nor  destroyed.  It  should  be  stated,  however,  that  the  general 
law  of  conservation  of  energy,  though  universally  accepted,  has 
not  been  proved  by  direct  experiment  in  all  cases;  there  may  be 
cases  that  are  not  susceptible  of  so  direct  a  proof  as  we  have  for 
the  transformation  of  heat  into  work. 

The  best  determinations  of  the  mechanical  equivalent  of  heat 
were  made  by  Rowland,  whose  work  will  be  considered  in  detail 
in  connection  with  the  properties  of  steam  and  water.  From 
his  work  it  appears  that  778  foot-pounds  of  work  are  required  to 
raise  one  pound  of  water  from  62°  to  63°  Fahrenheit;  this  value 
of  the  mechanical  equivalent  of  heat  is  now  commonly  accepted 
by  engineers,  and  is  verified  by  the  latest  determinations  by 
Joule  and  other  experimenters. 

The  values  of  the  mechanical  equivalent  of  heat  for  the  Eng- 
lish system  and  for  the  metric  system  are: 

i  B.  T.  u.  =  778  foot-pounds. 

i  calorie   =  426.9  metre- kilograms. 

This  physical  constant  is  commonly  represented  by  the  letter 
J\  the  reciprocal  is  represented  by  A. 

'3 


!4  FIRST    LAW    OF   THERMODYNAMICS 

In  older  works  on  thermodynamics  the  values  of  /  are  com- 
monly quoted  as  772  for  the  English  system  and  424  for  the 
metric  system.  The  error  of  these  values  is  about  one  per  cent. 

Effects  of  the  Transfer  of  Heat.  —  Let  a  quantity  of  any  sub- 
stance of  which  the  weight  is  one  unit  —  i.e.,  one  pound  or  one 
kilogram  —  receive  a  quantity  of  heat  dQ.  It  will,  in  general, 
experience  three  changes,  each  requiring  an  expenditure  of 
energy.  They  are:  (i)  The  temperature  will  be  raised,  and, 
according  to  the  theory  that  sensible  heat  is  due  to  the  vibra- 
tions of  the  particles  of  the  body,  the  kinetic  energy  will  be 
increased.  Let  dS  represent  this  change  of  sensible  heat  or 
vibration  work  expressed  in  units  of  work.  (2)  The  mean 
positions  of  the  particles  will  be  changed;  in  general  the  body 
will  expand.  Let  dl  represent  the  units  of  work  required  for 
this  change  of  internal  potential  energy,  or  work  of  disgregation. 
(3)  The  expansion  indicated  in  (2)  is  generally  against  an  exter- 
nal pressure,  and  to  overcome  the  same  —  that  is,  for  the  change 
in  external  potential  energy  —  there  will  be  required  the  work 
dW. 

If  during  the  transmission  no  heat  is  lost,  and  if  no  heat  is 
transformed  into  other  forms  of  energy,  such  as  sound,  electricity, 
etc.,  then  the  first  law  of  thermodynamics  gives 

dQ  =  A(dS  +  dl  +  dW) (15) 

It  is  to  be  understood  that  any  or  all  of  the  terms  of  the  equa- 
tion may  become  zero  or  may  be  negative.  If  all  the  terms 
become  negative  heat  is  withdrawn  instead  of  added,  and  dQ  is 
negative.  It  is  not  easy  to  distinguish  between  the  vibration 
work  and  the  disgregation  work,  and  for  many  purposes  it  is 
unnecessary;  consequently  they  are  treated  together  under  the 
name  of  intrinsic  energy,  and  we  have 

dQ  =  A  (dS  +  dl  +  dW)  =  A  (dE  +  dW)    .     .  (16) 

The  inner  work,  or  intrinsic  energy,  depends  on  the  state  of 
the  body,  and  not  at  all  on  the  manner  by  which  it  arrived  at 


EFFECTS    OF   THE    TRANSFER   OF    HEAT  15 

that  state;  just  as  the  total  energy  of  a  falling  body,  with  refer- 
ence to  a  given  plane  consisting  of  kinetic  energy  and  potential 
energy,  depends  on  the  velocity  of  the  body  and  the  height 
above  the  plane,  and  not  on  the  previous  history  of  the  body. 

The  external  work  is  assumed  to  be  done  by  a  fluid-pres- 
sure; consequently 

dW  =  pdv  ........   (17) 

W  =  fj'pdv      ......  (18) 

where  v2  and  vl  are  the  final  and  initial  volumes. 

In  order  to  find  the  value  of  the  integral  v  in  equation  (18)  it 
is  necessary  to  know  the  manner  in  which  the  pressure  varies 
with  the  volume.  Since  the  pressure  may  vary  in  different  ways, 
the  external  work  cannot  be  determined  from  the  initial  and 
final  states  of  the  body;  consequently  the  heat  required  to  effect 
a  change  from  one  state  to  another  depends  on  the  manner  in 
which  the  change  is  effected. 

Assuming  the  law  of  the  variation  of  the  pressure  and  volume 
to  be  known,  we  may  integrate  thus: 


.   .   .    .(19) 


In  order  to  determine  E  for  any  state  of  a  body  it  would  be 
necessary  to  deprive  it  entirely  of  vibration  and  disgregation 
energy,  which  would  of  course  involve  reducing  it  to  a  state  of 
absolute  cold;  consequently  the  direct  determination  is  impossi- 
ble. However,  in  all  our  work  the  substances  operated  on  are 
changed  from  one  state  to  another,  and  in  each  state  the  intrinsic 
energy  depends  on  the  state  only;  consequently  the  change  of 
intrinsic  energy  may  be  determined  from  the  initial  and  final 
states  only,  without  knowing  the  manner  of  change  from  one  to 
the  other. 

In  general,  equations  will  be  arranged  to  involve  differences 


i6 


FIRST    LAW    OF   THERMODYNAMICS 


of  energy  only,  and  the  hypothesis  involved  in  a  separation  into 
vibration  and  disgregation  work  avoided. 

Thermal  Lines.  —  The  external  work  can  be  determined  only 
when  the  relations  of  p  and  v  are  known,  or,  in  general,  when 
the  characteristic  equation  is  known.  It  has  already  been 
shown  that  in  such  case  the  equation  may  be  represented  by  a 
geometrical  surface,  on  which  so-called  thermal  lines  can  be 
drawn  representing  the  properties  of  the  substance  under  con- 
sideration. These  lines  are  commonly  projected  on  the  (p,  v) 
plane.  It  is  convenient  in  many  cases  to  find  the  relation  of  p 
and  v  under  a  given  condition  and  represent  it  by  a  curve  drawn 
directly  on  the  (p,  v)  plane. 

Lines  of  Equal  Pressure.  —  The  change  of 
condition  takes  place  at  constant  pressure,  and 
consists  of  a  change  of  volume,  as  represented  in 
Fig.  3.  The  tracing-  point  moves  from  al  to  02, 
and  the  volume  changes  from  vl  to  v2.  The 
work  done  is  represented  by  the  rectangular  area 
under  a^a^  or  by 


FIG.  3. 


W 


=  p  I    2  dv  =  p(v2  —  vj       ....   (20) 

%J  v\ 


During  the  change  the  temperature  may  or  may  not  change; 
the  diagram  shows  nothing  concerning  it. 

Lines  of  Equal  Volume.  —  The  pressure  in- 
creases at  constant  volume,  and  the  tracing-point 
moves  from  al  to  a2.  The  temperature  usually 
increases  meanwhile.  Since  dv  is  zero, 


W 


.    (21) 


a  a 


FIG.  4. 


Isothermal   Lines,    or   Lines   of   Equal    Temperature.  —  The 

temperature   remains   constant,   and   a   line  is   drawn,    usually 
convex,  toward  the  axis  OF.     The  pressure  of  a  mixture  of  a 


ADIABATIC    LINES  1 7 

liquid  and  its  vapor  is  constant  for  a  given  temperature;  con- 
sequently the  isothermal  for  such  a  mixture  is  a  line  of  equal 
pressure,  represented  by  Fig.  3.  The  iso- 
thermal of  a  perfect  gas,  on  the  other  hand,  is 
an  equilateral  hyperbola,  as  appears  from  the 
law  of  Boyle,  which  may  be  written 


pv  =  C.  FlG.  5. 

Isodynamic  or  Isoenergic  Lines  are  lines  representing  changes 
during  which  the  intrinsic  energy  remains  constant.  Conse- 
quently all  the  heat  received  is  transformed  into  external  work. 
It  will  be  seen  later  that  the  isodynamic  and  isothermal  lines 
for  a  gas  are  the  same. 

Adiabatic  Lines.  —  A  very  important  problem  in  thermo- 
dynamics is  to  determine  the  behavior  of  a  substance  when  a 
change  of  condition  takes  place  in  a  non-conducting  vessel. 
During  the  change  —  for  example,  an  increase  of  volume  or 
expansion  —  some  of  the  heat  in  the  substance  may  be  changed 
into  work;  but  no  heat  is  transferred  to  or  from  the  substance 
through  the  walls  of  the  containing  vessel.  Such  changes  are 
called  adiabatic  changes. 

Very  rapid  changes  of  dry  air  in  the  cylinder  of  an  air-com- 
pressor or  a  compressed-air  engine  are  very  nearly  adiabatic. 
Adiabatic  changes  never  occur  in  the  cylinder  of  a  steam-engine 
on  account  of  the  rapidity  with  which  steam  is  condensed  on  or 
vaporized  from  the  cast-iron  walls  of  the  cylinder. 

Since  there  is  no  transmission  of  heat  to  (or  from)  the  working 
substance,  equation  (19)  becomes 

'pdv)     ....  (22) 


E,  -  E2  =  fjj  pdv  ..........   (23) 

that  is,  the  external  work  is  done  wholly  at  the  expense  of  the 
intrinsic  energy  of  the  working  substance,  as  must  be  the  case 
in  conformity  with  the  assumption  of  an  adiabatic  change. 


i8 


FIRST    LAW    OF   THERMODYNAMICS 


FIG.  6. 


Relation  of  Adiabatic  and  Isothermal  Lines.  —  An  important 
property  of  adiabatic  lines  can  be  shown  to  advantage  at  this 

place,  namely,  that  such  a  line 
is  steeper  than  an  isothermal 
line  on  the  (p,  v)  plane  where 
they  cross,  as  represented  in 
Fig.  6.  The  essential  feature  of 
adiabatic  expansion  is  that  no 
heat  is  supplied  and  that  conse- 
quently the  external  work  of 
expansion  is  done  at  the  expense 
of  the  intrinsic  energy  which 
consequently  decreases.  The 
intrinsic  energy  is  the  sum  of 
the  vibration  energy  and  the 
disgregation  energy,  both  of 
which  in  general  decrease  during  an  adiabatic  expansion;  in  partic- 
ular the  decrease  of  vibration  energy  means  a  loss  of  temperature. 
Conversely  an  adiabatic  compression  is  accompanied  by  an  in- 
crease of  temperature.  If  an  isothermal  compression  is  repre- 
sented by  cb,  then  an  adiabatic  compression  will  be  represented 
by  a  steeper  line  like  ca,  crossing  the  constant  pressure  line  ba  to 
the  right  of  b,  and  thus  indicating  that  at  that  pressure  there  is 
a  greater  volume,  as  must  be  the  case  for  a  body  which  expands 
during  a  rise  of  temperature  at  constant  pressure. 

It  is  very  instructive  to  note  the  relation  of  these  lines  on  the 
surface  which  represents  the  characteristic  equation  for  a  perfect 
gas.  In  Fig.  6,  which  is  an  isometric  projection,  the  general 
form  of  the  surface  can  be  recognized  from  the  following  condi- 
tions:—  a  horizontal  section  representing  constant  pressure 
cuts  the  surface  in  a  straight  line  which  indicates  that  the  volume 
increases  proportionally  to  the  absolute  temperature,  and  this 
line  is  projected  as  a  horizontal  line  on  the  (p,  v)  plane ;  a  vertical 
section  parallel  to  the  (/>,  /)  plane  shows  that  the  pressure  in 
this  case  increases  as  the  absolute  temperature,  and  the  line  of 
intersection  with  the  surface  is  projected  as  a  vertical  line  on  the 


THERMAL    LINES    AND    THEIR    PROJECTIONS 


(p,  v)  plane;  finally  vertical  sections  parallel  to  the  (p,  v)  plane 
are  rectangular  hyperbolae  which  are  projected  in  their  true 
form  on  the  (p,  v)  plane.  If  AC  is  an  adiabatic  curve  on  the 
characteristic  surface,  its  loss  of  temperature  is  properly  repre- 
sented by  the  fact  that  it  crosses  a  series  of  isothermals  in  passing 
from  A  to  C;  A  B  is  a  line  of  constant  pressure  showing  a  decrease 
of  temperature  between  the  isothermals  through  A  and  through 
C;  finally  the  projection  of  ABC  on  to  the  (p,  v)  plane  shows  that 
the  adiabatic  line  ac  is  steeper  than  the  isothermal  line  be. 
Attention  should  be  called  to  the  fact  that  the  first  statement 
of  this  relation  is  the  more  general  as  it  holds  for  all  substances 
that  expand  with  rise  of  temperature  at  constant  pressure  what- 
ever may  be  the  form  of  the  characteristic  equation. 

Thermal  Lines  and  their  Projections.  —  The  treatment  given 
of  thermal  lines  is  believed  to  be  the  simplest  and  to  present 
the  features  that  are  most  useful  in  practice.  There  is,  how- 
ever, both  interest  and  instruction  in  considering  their  relation 
in  space  and  their  projections  on  the  three  thermal  planes.  It 
is  well  to  look  attentively  at  Fig.  6,  which  is  a  correct  isometric 
projection  of  the  characteristic  surface  of  a  gas  following  the 
law  of  Boyle  and  Gay-Lussac,  noting  that  every  section  by  a 
plane  parallel  to  the  (p,  v)  plane  is 
a  rectangular  hyperbola  which  has 
the  same  form  in  space  and  when 
projected  on  the  (p,  v)  plane.  The 
sections  by  a  plane  parallel  to  the 
(p,  /)  plane  are  straight  lines  and  are 
of  course  projected  as  straight  lines 
on  that  plane  and  on  the  (p,  v)  plane; 
in  like  manner  the  sections  by  planes 
parallel  to  the  (/,  v)  plane  are  straight 
lines.  The  adiabatic  line  in  space 
and  as  projected  on  the  (p,  v)  plane  is  probably  drawn  a  little 
too  steep,  but  the  divergence  from  truth  is  not  evident  to  the  eye. 

In  Fig.  7  the  same  method  of  projection  is  used,  but  other 
lines  are  added  together  with  their  projections  on  the  several 


20  FIRST    LAW    OF   THERMODYNAMICS 

planes.  Beginning  at  the  point  a  in  space  the  line  ab  is  an 
isothermal  which  is  projected  as  a  rectangular  hyperbola  a'b' 
on  the  (p,  v)  plane,  and  as  straight  lines  a"b"  and  a"'b'"  on 
the  (pj  /)  and  (/,  v)  plane.  The  adiabatic  line  ac  is  steeper 
than  the  isothermal,  both  in  space  and  on  the  (p,  v)  plane,  as 
already  explained;  it  is  projected  as  a  curve  (a"c"  or  a"'cr")  on 
the  other  planes.  The  section  showing  constant  pressure  is 
represented  in  space  by  the  straight  line  ae  which  projected  on 
the  (p,  /)  plane  is  parallel  to  the  axis  ot,  and  on  the  (/,  v) 
plane  is  parallel  to  the  line  itself  in  space;  on  the  (p,  v)  plane  it  is 
horizontal,  as  shown  in  Fig.  3.  In  much  the  same  way  ad  is  the 
section  by  a  plane  parallel  to  the  (/,  p)  plane,  and  a'd1 ',  a"drt 
and  a'"df"  are  its  projections. 

Graphical  Representations  of  Change  of  Intrinsic  Energy.  — 
Professor  Rankine  first  used  a  graphical  method  of  representing 
a  change  of  intrinsic  energy,  employing  adiabatic  lines  only,  as 
follows : 

Suppose  that  a  substance  is  originally  in  the  state  A  (Fig.  8), 
and  that  it  expands  adiabatically;  then  the  external  work  is  done 
at  the  expense  of  the  intrinsic  energy;  hence  if  the  expansion 
has  proceeded  to  A±  the  area  AA^^a,  which  represents  the 
external  work,  also  represents  the  change  of  intrinsic  energy. 
Suppose  that  the  expansion  were  to  continue  indefinitely;  then 
the  adiabatic  will  approach  the  axis  OF 
indefinitely,  and  the  area  representing  the 
work  will  be  included  between  the  curve  A  a 

„ ^    produced  indefinitely,   the  ordinate  A  a,   and 

^71 — ff  the  axis  OF;  this  area  will  represent  all  the 
<*i      work  that  can  be  obtained  by  the  expansion 
FlG>  8-  of  the  substance;  and  if  it  be  admitted  that 

during  the  expansion  all  the  intrinsic  energy  is  transformed 
into  work,  so  that  at  the  end  the  intrinsic  energy  is  zero,  it  rep- 
resents also  the  intrinsic  energy.  In  cases  for  which  the  equa- 
tion of  the  adiabatic  can  be  found  it  is  easy  to  show  that 

P<*v (24) 


CHANGE   OF   INTRINSIC    ENERGY  21 

is  a  finite  quantity;  and  in  any  case,  if  we  admit  an  absolute  zero 
of  temperature,  it  is  evident  that  the  intrinsic  energy  cannot 
be  infinite.  On  the  other  hand,  if  an  isothermal  curve  were 
treated  in  the  same  way  the  area  would  be  infinite,  since  heat 
would  be  continually  added  during  the  expansion. 

Now  suppose  the  body  to  pass  from  the  condition  represented 
by  A  to  that  represented  by  B,  by  any  path  whatever  —  that  is, 
by  any  succession  of  changes  whatever  —  for  example,  that 
represented  by  the  irregular  curve  AB.  The  intrinsic  energy 
in  the  state  B  is  represented  by  the  area  VbBfl.  The  change  of 
intrinsic  energy  is  represented  by  the  area  pBbaAa,  and  this 
area  does  not  depend  on  the  form  of  the  curve  AB.  This  graph- 
ical process  is  only  another  way  of  saying  that  the  intrinsic 
energy  depends  on  the  state  of  the  substance  only,  and  that 
change  of  intrinsic  energy  depends  on  the  final  and  initial  states 
only. 

Another  way  of  representing  change  of  intrinsic  energy  by 
aid  of  isodynamic  lines  avoids  an  infinite  diagram.     Suppose 
the  change  of  state  to  be  represented  by  the 
curve  A  B  (Fig.  9).      Draw  an  isodynamic 
line  AC  through  the  point  A,  and  an  adia- 
batic  line  BC  through  B,  intersecting  at  C; 
in  general  the  isoenergic  line  is  distinct 
from  the  isothermal  line;  for  example,  the 
isothermal  line  for  a  saturated  vapor  is  a  FIG.  9. 

straight  line  parallel  to  the  OV  axis,  and 
the  isoenergic  line  is  represented  approximately  by  the  equation 

pv  1'0456  =  const. 

Then  the  avoa  Abba  represents  the  external  work,  and  the  area 
bBCc  represents  the  change  of  intrinsic  energy;  for  if  the  body  be 
allowed  to  expand  adiabatically  till  the  intrinsic  energy  is  reduced 
to  its  original  amount  at  the  condition  represented  by  A  the 
external  work  bBCc  will  be  done  at  the  expense  of  the  intrinsic 
energy. 


CHAPTER   III. 

SECOND   LAW   OF  THERMODYNAMICS. 

Heat-engines  are  engines  by  which  heat  is  transformed  intc 
work.  All  actual  engines  used  as  motors  go  through  continuous 
cycles  of  operations,  which  periodically  return  things  to  the 
original  conditions.  All  heat-engines  are  similar  in  that  they 
receive  heat  from  some  source,  transform  part  of  it  into  work, 
and  deliver  the  remainder  (minus  certain  losses)  to  a  refrigerator. 
The  source  and  refrigerator  of  a  condensing  steam-engine  are 
the  furnace  and  the  condenser.  The  boiler  is  properly  con- 
sidered as  a  part  of  the  engine,  and  receives  heat  from  the  source. 
Carnot's  Engine.  —  It  is  convenient  to  discuss  a  simple  ideal 
engine,  first  described  by  Carnot. 

Let  P  of  Fig.  10  represent  a  cylinder  with  non-conducting 
walls,  in  which  is  fitted  a  piston,  also  of  non-conducting  material, 

and  moving  without  friction;  on  the 
other  hand,  the  bottom  of  the  cylinder 
is  supposed  to  be  of  a  material  that  is 
a  perfect  conductor.  There  is  a  non- 
conducting stand  C  on  which  the 
cylinder  can  be  placed  while  adiabatic 
changes  take  place.  The  source  of 

heat  A  Sit  a,  temperature  /  is  supposed  to  be  so  maintained 
that  in  operations  during  which  the  cylinder  is  placed  on  it, 
and  draws  heat  from  it,  the  temperature  is  unchanged.  The 
refrigerator  B  at  the  temperature  /t  in  like  manner  can  with- 
draw heat  from  the  cylinder,  when  it  is  placed  on  it,  at  a 
constant  temperature. 

Let  there  be  a  unit  of  weight  (for  example,  one  pound)  of  a 
certain  substance  in  -  the  cylinder  at  the  temperature  t  of  the 
source  of  heat.  Place  the  cylinder  on  the  source  of  heat  A 

22 


CARNOTS    ENGINE 


(Fig.  10),  and  let  the  substance  expand  at  the  constant  tem- 
perature /,  receiving  heat  from  the  source  A. 
If    the  first  condition  of    the  substance  be 
represented  by  A    (Fig.  u),  then  the  second 
will  be  represented  by  B,  and  AB  will  be  an 
isothermal.     If    Ea  and  Eb  are  the  intrinsic 
energies  at  A  and  B,  and  if  Wab,  represented 
by  the  area  aABb,  be  the  external  work,  the 
heat  received  from  A  will  be 


FIG.  ii. 


=  A(Eb-Ea    +  Wab) 


(25) 


Now  place  the  cylinder  on  the  stand  C  (Fig.  10),  and  let 
the  substance  expand  adiabatically  until  the  temperature  is 
reduced  to  tlt  that  of  the  refrigerator,  the  change  being  rep- 
resented by  the  adiabatic  BC  (Fig.  n).  If  Ec  is  the  intrinsic 
energy  at  C,  then,  since  no  heat  passes  into  or  out  of  the 

cylinder, 

o  =  A  (Ec-Eb  +  Wbc)    .....  (26) 

where  Wbc  is  the  external  work  represented  by  the  area  bBCc. 
Place  the  cylinder  on  the  refrigerator  B,  and  compress  the  sub- 
stance till  it  passes  through  the  change  represented  by  CD, 
yielding  heat  to  the  refrigerator  so  that  the  temperature  remains 
constant.  If  Ed  is  the  intrinsic  energy  at  D,  then 


-Q,  =  A  (Ed-Ec-  Wcd) 


(27) 


is  the  heat  yielded  to  the  refrigerator,  and  Wcd,  represented  by 
the  area  cCDd,  is  the  external  work,  which  has  a  minus  sign, 
since  it  is  done  on  the  substance. 

The  point  D  is  determined  by  drawing  an  adiabatic  from  A 
to  intersect  an  isothermal  through  C.  The  process  is  completed 
by  compressing  the  substance  while  the  cylinder  is  on  the  stand 
C  (Fig.  10)  till  the  temperature  rises  to  /,  the  change  being 
represented  by  the  adiabatic  DA.  Since  there  is  no  transfer 
of  heat, 

o  =  A   (Ea-  Ed-  Wda) (28) 


24  SECOND    LAW    OF   THERMODYNAMICS 

Adding  together  the  several  equations,  member  to  member, 
Q-Q1  =  A(Wab  +  Wlc  -  Wcd  -  Wda)    .     .  (29) 

or,  if  W  be  the  resulting  work  represented  by  the  area  ABCD, 
then 

(30) 


that  is,  the  difference  between  the  heat  received  and  the  heat 
delivered  to  the  refrigerator  is  the  heat  transformed  into  work. 

A  Reversible  Engine  is  one  that  may  run  either  in  the  usual 
manner,  transforming  heat  into  work,  or  reversed,  describing 
the  same  cycle  in  the  opposite  direction,  and  transforming  work 
into  heat. 

A  Reversible  Cycle  is  the  cycle  of  a  reversible  engine. 

Carnot's  engine  is  reversible,  the  reversed  cycle  being 
ADCBA  (Fig.  n),  during  which  work  is  done  by  the  engine 
on  the  working  substance.  The  engine  then  draws  from  the 
refrigerator  a  certain  quantity  of  heat,  it  transforms  a  certain 
quantity  of  work  into  heat,  and  delivers  the  sum  of  both  to  the 
source  of  heat. 

No  actual  heat-engine  is  reversible  in  the  sense  just  stated, 
for  when  the  order  of  operations  can  be  reversed,  changing  the 
engine  from  a  motor  into  a  pump  or  compressor,  the  reversed 
cycle  differs  from  the  direct  cycle.  For  example,  the  valve- 
gear  of  a  locomotive  may  be  reversed  while  the  train  is  running, 
and  then  the  cylinders  will  draw  gases  from  the  smoke-box, 
compress  them,  and  force  them  into  the  boiler.  The  locomotive 
as  ordinarily  built  is  seldom  reversed  in  this  way,  as  the  hot 
gases  from  the  smoke-box  injure  the  surfaces  of  the  valves  and 
cylinders.  Some  locomotives  have  been  arranged  so  that  the 
exhaust-  nozzles  can  be  shut  off  and  steam  and  water  supplied 
to  the  exhaust-pipe,  thus  avoiding  the  damage  from  hot  gases 
when  the  engine  is  reversed  in  this  way.  Such  an  engine  may 
then  have  a  reversed  cycle,  drawing  steam  into  the  cylinders, 
compressing  and  forcing  it  into  the  boiler;  but  in  any  case  the 


EFFICIENCY 


reversed  cycle  differs  from  the  direct  cycle,  and  the  engine  is 
not  properly  a  reversible  engine. 

A  Closed  Cycle  is  any  cycle  in  which  the  final  state  is  the  same 
as  the  initial  state.  Fig.  12  represents  such  a 
cycle  made  up  of  four  curves  of  any  nature 
whatever.  If  the  four  curves  are  of  two  species 
only,  as  in  the  diagram  representing  the  cycle 
of  Carnot  's  engine,  the  cycle  is  said  to  be  simple. 
In  general  we  shall  have  for  a  cycle  like  that  of  Fig.  12, 


Qab  +  Qlc  ~  Qcd  ~  Qda 


FIG.  12. 


=  A    (W\ 


FIG.  13  • 


A  closed  curve  of  any  form  may  be  consid- 
ered to  be  the  general  form  of  a  closed  cycle, 
as  that  in  Fig.  13.  For  such  a  cycle  we  have 

I  dQ  =  A  I  dW,  which   is    one  more  way  of 

stating  the  first  law  of  thermodynamics. 

It  may  make  this  last  clearer  to  consider  the  cycle  of  Fig.  14 
composed  of  the  isothermals  AB,  CD,  and  EG,  and  the 
adiabatics  BC,  DE,  and  GA.  The  cycle 
may  be  divided  by  drawing  the  curve 
through  from  C  to  F.  It  is  indifferent 
whether  the  path  followed  be  A  BCD  EG  A 
or  ABCFCDEGA,  or,  again,  ABCFGA  + 
CDEFC. 

Again,  an  irregular  figure  may  be 
imagined  to  be  cut  into  elementary  areas  by  isothermals  and 
adiabatic  lines,  as  in  Fig.  15.  The  summation  of  the  areas  will 
give  the  entire  area,  and  the  summation  of  the  works  represented 
by  these  will  give  the  entire  work  represented  by  the  entire  area. 

The  Efficiency  of  an  engine  is  the  ratio  of  the  heat  changed 
into  work  to  the  entire  heat  applied ;  so  that  if  it  be  represented 
by  e, 

AW 

e"  ~Q          Q 


FIG.  14. 


26  SECOND    LAW    OF   THERMODYNAMICS 

for  the  heat  Q'  rejected  to  the  refrigerator  is  what  is  left  after 
AW  thermal  units  have  been  changed  into  work. 

Carnot's  Principle.  —  It  was  first  pointed 
out  by  Carnot  that  the  efficiency  of  a 
reversible  engine  does  not  depend  on  the 
nature  of  the  working  substance,  but  that 
it  depends  on  the  temperatures  of  the 
,  source  of  heat  and  the  refrigerator. 


FlG>  I5<  Let  us  see  what    would    be    the    conse- 

quence   if    this    principle    were    not    true. 

Suppose  there  are  two  reversible  engines  R  and  A,  each  taking 
Q  thermal  units  per  second  from  the  source  of  heat,  of  which 
A  is  the  more  efficient,  so  that 


is  larger  than 

AWr 


(33) 


this  can  happen  only  because  Qd  is  less  than  Q/,  for  Q  is  assumed 
to  be  the  same  for  each  engine.  Let  the  engine  R  be  reversed 
and  coupled  to  A,  which  can  run  it  and  still  have  left  the  useful 
work  Wa  —  Wr.  This  useful  work  cannot  come  from  the 
source  of  heat,  for  the  engine  R  when  reversed  gives  to  the  source 
Q  thermal  units  per  second,  and  A  takes  the  same  amount  in  the 
same  time.  It  must  be  assumed  to  come  from  the  refrigerator, 
which  receives  Qa'  thermal  units  per  second,  and  gives  up  Qr' 
thermal  units  per  second,  so  that  it  loses 

C/  -  QJ  =  A  (Wa  -  Wr) 

thermal  units  per  second.  This  equation  may  be  derived  from 
equations  (32)  and  (33)  by  subtraction. 

Now  it  cannot  be  proved  by  direct  experiment  that  such  an 
action  as  that  just  described  is  impossible.  Again,  the  first  law 
of  thermodynamics  is  scrupulously  regarded,  and  there  is  no 


SECOND    LAW    OF    THERMODYNAMICS  27 

contradiction  or  formal  absurdity  of  statement.  And  yet  when 
the  consequences  of  the  negation  of  Carnot's  principles  are 
clearly  set  forth  they  are  naturally  rejected  as  improbable,  if  not 
impossible.  The  justification  of  the  principle  is  found  in  the 
fact  that  theoretical  deductions  from  it  are  confirmed  by 
experiments. 

Second  Law  of  Thermodynamics.  —  The  formal  statement 
of  Carnot's  principle  is  known  as  the  second  law  of  thermody- 
namics. Various  forms  are  given  by  different  investigators, 
none  of  which  are  entirely  satisfactory,  for  the  conception  is  not 
simple,  as  is  that  of  the  first  law. 

The  following  are  some  of  the  statements  of  the  second  law : 

(1)  All  reversible  engines  working  between  the  same  source  of 
heat  and  refrigerator  have  the  same  efficiency. 

(2)  The  efficiency  of  a  reversible  engine  is  independent  of  the 
working  substance. 

(3)  A  self-acting  machine  cannot  convey  heat  from  one  body 
to  another  at  a  higher  temperature. 

The  second  law  is  the  third  general  principle  of  thermody- 
namics; it  differs  from  each  of  the  others  and  is  independent 
of  them.  Summing  up  briefly,  the  first  general  principle  is  a 
pure  assumption  that  thermodynamic  equations  may  contain 
only  two  independent  variables;  the  second  is  the  statement  of 
an  experimental  fact;  the  third  is  a  choice  of  one  of  two 
propositions  of  a  dilemma.  The  first  and  third  are  justified 
by  the  results  of  the  applications  of  the  theory  of  thermo- 
dynamics. 

So  far  as  efficiency  is  concerned,  the  second  law  of  thermo- 
dynamics shows  that  it  would  be  a  matter  of  indifference  what 
working  substance  should  be  chosen;  we  might  use  air  or  steam 
in  the  same  engine  and  get  the  same  efficiency  from  either; 
there  would,  however,  be  a  great  difference  in  the  power  that 
would  be  obtained.  In  order  to  obtain  a  diagram  of  convenient 
size  and  distinctness,  the  adiabatics  are  made  much  steeper  than 
the  isothermals  in  Fig.  n ;  as  a  matter  of  fact  the  diagram  drawn 
correctly  is  so  long  and  attenuated  that  it  would  be  practically 


28  SECOND    LAW    OF   THERMODYNAMICS 

worthless  even  if  it  could  be  obtained  with  reasonable  approxi- 
mation in  practice,  as  the  work  of  the  cycle  would  hardly  over- 
come the  friction  of  the  engine.  The  isothermals  for  a  mixture 
of  water  and  steam  are  horizontal,  and  the  diagram  takes  the 
form  shown  by  Fig.  16.  In  practice  a  dia- 
gram closely  resembling  Carnot's  cycle  is 
chosen  as  the  ideal,  differing  mainly  in  that 
steam  is  assumed  to  be  supplied  and  ex- 
hausted. In  a  particular  case  an  engine 

FIG.  16. 

working  between  the  temperatures  3 62°. 2  F. 
and  158°  F.  had  an  actual  thermal  efficiency  of  0.18;  the 
ideal  cycle  had  an  efficiency  of  0.23,  and  Carnot's  cycle  had 
an  efficiency  of  0.25.  The  ratio  of  0.18  to  0.23  is  about  0.81, 
which  compares  favorably  with  the  efficiency  of  turbine  water- 
wheels. 

Carnot's  Function.  —  Carnot  's  principle  asserts  that  the 
efficiency  of  a  reversible  engine  is  independent  of  the  nature  of 
the  working  substance;  consequently  the  expression  for  the 
efficiency  will  not  include  such  properties  of  the  working  sub- 
stance as  specific  volume  and  specific  pressure.  But  the  prin- 
ciple asserts  also  that  the  efficiency  depends  on  the  temperatures 
of  the  source  of  heat  and  the  refrigerator,  which  indeed  are  the 
only  properties  of  the  source  and  refrigerator  that  can  affect 
the  working  of  the  engine. 

We  may  then  represent  the  efficiency  as  a  function  of  the  tem- 
peratures of  the  source  of  heat  and  the  refrigerator,  or,  what 
amounts  to  the  same  thing,  as  a  function  of  the  superior  tem- 
perature and  the  difference  of  the  temperatures,  and  may  write 

AW  _  Q  —Q' 
e  =     Q  Q       -  -F  ft  *  -  O 

where  Q  is  the  heat  received,  Q'  the  heat  rejected,  and  /  and  if 
are  the  temperatures  of  the  source  of  heat  and  of  the  refrigerator- 
on  any  scale  whatsoever,  absolute  or  relative. 

If  the  temperature  of  the  refrigerator  approaches  near  that  of 


KELVIN'S    GRAPHICAL   METHOD 


29 


the  source  of  heat  Q  —  Q'  and  /  —  tf  become 
the  limit  dQ  and  dt,  so  that 


and  A/,  and  at 

'   .     .    (34) 


It  is  convenient  to  assume  that  the  equation  can  be  expressed 
in  the  form 

£ 


/«* 


The  function/  (/)  is  known  as  Carnot's  function,  and  physi- 
cists consider  that  the  isolation  of  this  function  and  the  relation 
of  the  function  to  temperature  are  of  great  theoretical  importance. 

Absolute  Scale  of  Temperature.  —  It  is  convenient  and  cus- 

tomary to  assign  to  Carnot's  function  the  form  -  ,  where  T  -is 

the  temperature  by  the  absolute  scale  referred  to  on  page  3, 
measured  from  the  absolute  zero  of  temperature.  This  assump- 
tion is  justified  by  the  facts  that  the  theory  of  thermodynamics 
is  much  simplified  thereby,  and  that  the  difference  between 
such  a  scale  of  temperature  and  the  scale  of  the  air-thermometer 
is  very  small. 

Kelvin's  Graphical  Method.  —  This  treatment  of  Carnot  's 
function  was  first  proposed  by  Lord  Kelvin,  who  illustrated  the 
general  conception  by  the  following  graphical  construction: 

In  Fig.  17  let  ak  and  bi  be  two  adiabatic  lines,  and  let  the 
substance  have  its  condition 
represented  by  the  point  a. 
Through  a  and  d  draw  iso- 
thermal lines  ;  then  the  diagram 
abed  represents  the  cycle  of  a 
simple  reversible  engine.  Draw 
the  isothermal  line  fe,  so  that 
the  area  dcef  shall  be  equal  to 


FIG.  17. 


abed]    then    the   diagram    dcef 

represents     the    cycle  of  a  reversible   engine,  doing    the   same 

amount  of  work  per  stroke  as  that  engine  whose  cycle  is  repre- 


^ 

OF    THE  \ 

UNIVERSITY    ) 
/ 


SECOND    LAW    OF   THERMODYNAMICS 


sented  by  abed]  and  the  difference  between  the  heat  drawn 
from  the  source  and  delivered  to  the  refrigerator  —  i.e.,  the  heat 
transformed  into  work  —  is  the  same.  The  refrigerator  of  the 
first  engine  might  serve  for  the  source  of  heat  for  the  second. 

Suppose  that  a  series  of  equal  areas  are  cut  off  by  isothermal 
lines,  SiS/egh,  hgik,  etc.,  and  suppose  there  are  a  series  of  reversible 
engines  corresponding;  then  there  will  be  a  series  of  sources  of 
heat  of  determinate  temperatures,  which  may  be  chosen  to 
establish  a  thermometric  scale.  In  order  to  have  the  scale  cor- 
respond with  those  of  ordinary  thermometers,  one  of  the  sources 
of  heat  must  be  at  the  temperature  of  boiling  water,  and  one  at 
that  of  melting  ice;  and  for  the  centigrade  scale  there  will  be  one 
hundred,  and  for  the  Fahrenheit  scale  one  hundred  and  eighty, 
such  cycles,  with  the  appropriate  sources  of  heat,  between  boiling- 
point  and  freezing-point.  To  establish  the  absolute  zero  of  the 
scale  the  series  must  be  imagined  to  be  continued  till  the  area 
included  between  an  isothermal  and  the  two  adiabatics,  continued 
indefinitely,  shall  not  be  greater  than  one  of  the  equal  areas. 

This  conception  of  the  absolute  zero 
may  be  made  clearer  by  taking  wide 
intervals  of  temperature,  as  on  Fig. 
1 8,  where  the  cycle  abed  is  assumed 
to  extend  between  the  isothermals  of 
o°  and  100°  C. ;  that  is,  from  freez- 
ing-point to  boiling-point.  The 
next  cycle,  cdef,  extends  to  —  100°  C., 
and  the  third  cycle,  efgh,  extends 
to  —  200°  C.  The  remaining  area, 
which  is  of  infinite  length  and  ex- 
tremely attenuated,  is  bounded  by  the 
isothermal  gh  and  the  two  adiabatics 
-200  ha  and  gp.  The  diagram  of  course 
cannot  be  completed,  and  conse- 
quently the  area  cannot  be  measured; 

but  when  the  equations  to  the  isothermal  and  the  adiabatics 
are  known  it  can  be  computed.  So  computed,  the  area  is  found 


SPACING    OF   ADIABATICS 


to  be  --  Of  one  of  the  three  equal  areas  abed,  cdfe,  and  efhg. 
100 

The  absolute  zero  is  consequently  273°  C.  below  freezing-point. 
Further  discussion  of  the  absolute  scale  will  be  deferred  till 
a  comparison  is  made  with  the  air- thermometer. 

Spacing  of  Adiabatics.  —  Kelvin 's  graphical  scale  of  temper- 
ature is  clearly  a  method  of  spacing  isothermals  which  depends 
only  on  our  conceptions  of  thermodynamics  and  on  the  funda- 
mental units  of  weight  and  length.  Evidently  the  same  method 
may  be  applied  to  spacing  adiabatics,  and  thereby  a  new  concep- 
tion of  great  importance  may  be  introduced  into  the  theory  of 
thermodynamics.  On  this  conception  is  based  the  method  for 
solving  problems  involving  adiabatic  expansion  of  steam,  as 
will  be  explained  in  the  discussion  of  that  subject. 

In  Fig.  19  let  an  and  do 
be  two  isothermals,  and  let 
ad,  be,  Im  and  no  be  a  series 
of  adiabatics,  so  drawn  that 
the  areas  of  the  figures  abed, 
blmc,  and  Inom  are  equal; 
then  we  have  a  series  of 
adiabatics  that  are  spaced  in 
the  same  manner  as  are  the 
isothermals  in  Figs.  17  and 


1 8,  and,  as    with    those    iso- 
thermals, the  spacing  depends  only  on  our  conceptions  of  ther- 
modynamics and  the  fundamental  units  of  weight  and  length. 

In  the  discussion  of  Figs.  17  and  18  it  was  shown  that  the  area 
of  the  strip  between  the  initial  isothermal  ab  and  the  two  adiabatic 
lines  must  be  treated  as  finite,  and  that  in  consequence  the 
graphical  process  leads  to  an  absolute  zero  of  temperature.  On 
the  contrary,  the  area  between  the  adiabatic  ad  and  the  two 
isothermals  an  and  do  if  extended  infinitely  will  be  infinite,  and 
it  will  be  found  that  there  is  no  limit  to  the  number  of  adia- 
batics that  can  be  drawn  with  the  spacing*  indicated.  A  like 
result  will  follow  if  the  isothermals  are  extended  to  the  right  and 


32  SECOND   LAW   OF  THERMODYNAMICS 

upward,  and  if  adiabatics  are  spaced  off  in  the  same  manner. 
This  conclusion  comes  from  the  fact  pointed  out  on  page  21, 
that  the  area  under  an  isothermal  curve  which  is  extended  with- 
out limit  is  infinite,  because  heat  is  continuously  supplied,  some 
part  of  which  can  be  changed  into  work. 

It  is  convenient  to  introduce  a  new  function  at  this 
place  which  shall  express  the  spacing  of  adiabatics  as 
represented  in  Fig.  19,  and  which  will  be  called  entropy. 
From  what  precedes  it  is  evident  that  entropy  has  the 
same  relations  to  the  adiabatics  of  'Fig.  19  that  temperature 
has  to  the  isothermals  of  Figs.  17  and  18,  but  that  there  is  this 
radical  difference,  that  while  there  is  a  natural  absolute  zero  of 
temperature,  there  is  no  zero  of  entropy.  Consequently  in  prob- 
lems we  shall  always  deal  with  differences  of  entropy,  and  if  we 
find  it  convenient  to  treat  the  entropy  of  a  certain  condition  of  a 
given  substance  as  a  zero  point  it  is  only  that  we  may  count  up 
and  down  from  that  point. 

If  the  adiabatic  line  ad  in  Fig.  19  should  be  extended  to  the 
right,  it  would  clearly  lie  beneath  the  adiabatic  no,  which  agrees 
with  the  tacit  convention  of  that  figure,  i.e.,  that  as  spaced  the 
adiabatics  are  to  be  numbered  toward  the  right  and  that  the 
entropy  increases  from  a  toward  n. 

The  simplest  and  the  most  natural  definition  of  entropy  from 
the  present  considerations,  is  that  entropy  is  that  function  which 
remains  constant  for  any  change  represented  by  a  reversible 
adiabatic  expansion  (or  compression).  With  this  definition  in 
view,  the  adiabatic  lines  might  be  called  isoentropic  lines.  It 
should  be  borne  in  mind  that  our  present  discussion  is  purposely 
limited  to  expansion  in  a  non-conducting  cylinder  closed  by  a 
piston,  or  to  like  operations.  More  complex  operations  than 
that  just  mentioned  may  require  an  extension  of  the  conception 
of  entropy  and  lead  to  fuller  definitions.  Such  extensions  of  the 
conception  of  entropy  have  been  found  very  fruitful  in  certain 
physical  investigations,  and  many  writers  on  thermodynamics 
for  engineers  consider  that  they  get  like  advantages  from  them. 
There  is,  however,  an  advantage  in  limiting  the  conception  of  a 


GRAPHICAL   REPRESENTATION    OF    EFFICIENCY 


33 


new  function,  however  simple  that  conception  may  be  ;  and  there 
is  an  added  advantage  in  being  able  to  return  to  a  simple  con- 
ception at  will. 

Efficiency   of   Reversible   Engines.  —  Returning   to   equation 

(34)  and  replacing  Carnot's  function/  (/)  by  —  ->  as  agreed,  we 

have  for  the  differential  equation  of  the  efficiency  of  a  reversible 
engine 


= 
"~  T 


or,    integrating   between   limits, 


Q 


Tf 


and  the  efficiency  for  the  cycle  becomes 
Q  —  Qf       T  —  T' 
Q  T 


(35) 


This  result  might  have  been  obtained  before  (or  without)  the 
discussion  of  Kelvin 's  graphical  method,  and  leads  to  the  same 
conclusion,  that  the  absolute  temperature  can  be  made  to  depend 
on  the  efficiency  of  Carnot's  cycle,  and  may,  therefore,  be  inde- 
pendent of  any  thermometric  substance. 
As  has  already  been  said,  this  conception 
is  more  important  on  the  physical  side 
than  on  the  engineering  side,  and  its  reit- 
eration need  not  be  considered  to  call  for 
any  speculation  by  the  student  at  this  time. 

Graphical  Representation  of  Efficiency. 
—  Let  Fig.  20  represent  the  cycle  of 
a  reversible  heat-engine.  For  convenience 
it  is  supposed  there  are  four  degrees  of  temperature  from  the 
isothermal  AB  to  the  isothermal  DC,  and  that  there  are  three 
intervals  or  units  of  entropy  between  the  adiabatics  AD  and 


FIG.  20. 


34  SECOND    LAW    OF   THERMODYNAMICS 

EC.  First  it  will  be  shown  that  all  the  small  areas  into  which 
the  cycle  is  divided  by  drawing  the  intervening  adiabatics  and 
isothermals  are  equal.  Thus  we  have  to  begin  with  a  =  b  and 
a  =  c  by  construction.  But  engines  working  on  the  cycles  a 
and  b  have  the  same  efficiency  and  reject  the  same  amounts 
of  heat.  These  heats  rejected  are  equal  to  the  heats  supplied 
to  engines  working  on  the  cycles  c  and  d,  which  consequently 
take  in  the  same  amounts  of  heat.  But  these  engines  work 
between  the  same  limits  of  temperature  and  have  the  same 
efficiency,  and  consequently  change  the  same  amount  of  heat 
into  work.  Therefore  the  areas  c  and  d  are  equal.  In  like 
manner  all  the  small  areas  are  equal,  and  each  represents  one 
thermal  unit,  or  778  foot-pounds  of  work. 

It  is  evident  that  the  heat  changed  into  work  is  represented  by 

(T  -  T')  ($'  -  </>), 

and,  further,  that  the  same  expression  would  be  obtained  for  a 
similar  diagram,  whatever  number  of  degrees  there  might  be 
between  the  isothermals,  or  intervals  of  entropy  between  the 
adiabatics,  and  that  it  is  not  invalidated  by  using  fractions  of 
degrees  and  fractions  of  units  of  entropy.  It  is  consequently 
the  general  expression  for  the  heat  changed  into  work  by  an 
engine  having  a  reversible  cycle. 

It  is  clear  that  the  work  done  on  such  a  cycle  increases  as  the 
lower  temperature  T'  decreases,  and  that  it  is  a  maximum  when 
J1'  becomes  zero,  for  which  condition  all  of  the  heat  applied  is 
changed  into  work.  Therefore  the  heat  applied  is  represented 
by 

Q  =  T  &  -  <£), 

and  the  efficiency  of  the  engine  working  on  the  cycle  represented 
by  Fig.  20  is 

AW  =  Q  -  Q'  =  (T—T*)(<I>'  -  0)  =  T-  T 
Q  Q  T  &  -  <£)  T 

as  found  by  equation  (35).  The  deduction  of  this  equation  by 
integration  is  more  simple  and  direct,  but  the  graphical  method 


EXPRESSION    FOR   ENTROPY 


35 


is  interesting  and  may  give  the  student  additional  light  on  this 
subject. 

Temperature-Entropy  Diagram.  —  Thermal  diagrams  are  com- 
monly drawn  with  pressure  and  volume  for  the  co-ordinates, 
but  for  some  purposes  it  is  convenient  to  use  other  properties 
as  co-ordinates,  in  particular  temperature  and  entropy.  For 
example,  Fig.  21  represents  Carnot's  cycle 
drawn  with  entropies  for  abscissae  and  tem- 
peratures for  ordinates,  with  the  advantage 
that  indefinite  extensions  of  the  lines  are 
avoided,  and  the  areas  under  consideration 
are  evidently  finite  and  measurable.  With  0 
the  exception  that  there  appears  now  to  be  no  FlG-  «• 

necessity  to  show  that  the  areas  obtained  by  subdivision  are  all 
equal,  the  discussion  for  Fig.  20  drawn  with  pressures  and  vol- 
umes may  be  repeated  with  temperatures  and  entropies. 

Expression  for  Entropy.  —  One  advantage  of  using  the  tem- 
perature-entropy diagram  is  that  it  leads  at  once  to  a  method 
for  computing  changes  of  entropy.  Thus  in  Fig.  22  let  AB 
represent  an  isothermal  change,  and  let  A  a 
and  Bb  be  adiabatics  drawn  to  the  axis  of  <£; 
then  the  diagram  ABba  may  be  considered  to 
be  the  cycle  for  a  Carnot's  engine  working 
between  the  temperature  T  and  the  absolute 
-^zero,  and  consequently  having  the  efficiency 
unity.  The  heat  changed  into  work  may  there- 


FIG.  aa. 


fore  be  represented  by 


(36) 


If  we  are  dealing  with  a  change  under  any  other  condition 
than  constant  temperature,  we  may  for  an  infinitesimal  change, 
write  the  expression 


d(f>  = 


_dQ 


(37) 


and  for  the  entire  change  may  express  the  change  of  entropy  by 

*-*-/?. 


36  SECOND    LAW    OF   THERMODYNAMICS 

which  should  for  any  particular  case  either  be  integrated 
between  limits  or  else  a  constant  of  integration  should  be 
determined. 

Attention  should  be  called  to  the  fact  that  the  conception  of 
the  spacing  of  isothermals  and  adiabatics  is  based  fundamen- 
tally on  Carnot's  cycle  and  the  second  law  of  thermodynamics, 
which  has  been  applied  only  to  reversible  operations.  The 
method  of  calculating  changes  of  entropy  applies  in  like  manner 
to  reversible  operations;  and  when  entropy  is  employed  for 
calculations  of  operations  that  are  not  reversible,  discretion 
must  be  used  to  avoid  inconsistency  and  error. 

On  the  other  hand,  the  entropy  of  a  unit  weight  of  a  given 
substance  under  certain  conditions  is  a  perfectly  definite  quan- 
tity and  is  independent  of  the  previous  history  of  the  substance. 
This  may  be  made  evident  by  the  consideration  that  any  point 
on  the  line  no,  Fig.  19,  page  31,  has  a  certain  number  of  units  of 
entropy  (for  example,  three)  more  than  that  of  any  point  on 
the  adiabatic  ad. 

Example.  —  There  may  be  an  advantage  in  giving  a  calcu- 
lation of  a  change  of  entropy  to  emphasize  the  point  that  it  can 
be  represented  by  a  number.  Let  it  be  required  to  find  the 
change  of  entropy  during  an  isothermal  expansion  of  one  pound 
air  from  four  cubic  feet  to  eight  cubic. 

The  heat  applied  may  be  obtained  by  integrating  the  expression 

, ,       dQ       Idv  ,p  dv 

d<l>  =  -f  =    —  -   (Cp—cv)^—, 

the  value  of  the  latent  heat  having  been  taken  from  page  12. 
From  the  characteristic  equation 

pv  =  RT 
the  above  expression  may  be  reduced  to 


APPLICATION   TO   A    REVERSIBLE   CYCLE 


37 


or 


>>  —  <j>  =  (Cp  —  Cv)  log,  - 

g 

<j)  =  (0.2375  —  0.1690)  loge  -  =0.0475. 

4 


FIG.  23. 


A  problem  for  air  is  chosen  because  it  can  be  readily  worked 
out  at  this  place;  as  a  matter  of  fact,  there  are  few  occasions  in 
practice  where  there  is  reason  to  refer  to  entropy  of  air. 

Application  to  a  Reversible  Cycle.  —  A  very  important  result 
is  obtained  by  the  application  of  equation  (37)  to  the  calcula- 
tion of  entropy  during  a  reversible  cycle.  In  the  first  place, 
it  is  clear  that  the  entropy  of  a  substance  having  its  condition 
represented  by  the  point  a  (Fig.  23),  depends  on  the  adiabatic 
line  drawn  through  it;  in  other  words,  the  entropy  depends  only 
on  the  condition  of  the  substance. 
In  this  regard  entropy  is  like  intrin- 
sic energy  and  differs  from  external 
work.  Suppose  now  that  the  sub- 
stance is  made  to  pass  through  a 
cycle  of  operations  represented  by 
the  point  a  tracing  the  diagram  on 
Fig.  23;  it  is  clear  that  the  entropy  will  be  the  same  at  the  end 
of  the  cycle  as  at  the  beginning,  for  the  tracing-point  will  then 
be  on  the  original  adiabatic  line.  As  the  tracing-point  moves 
toward  the  right  from  adiabatic  to  adiabatic  the  entropy 
increases,  and  as  it  moves  to  the  left  the  entropy  decreases,  the 
algebraic  sum  of  changes  of  entropy  being  zero  for  the  entire 
cycle.  This  conclusion  holds  whether  the  cycle  is  reversible 
or  non-reversible.  The  cycle  represented  by  Fig.  23  is  purposely 
drawn  like  a  steam-engine  indicator  diagram  (which  is  not 
reversible)  to  emphasize  the  fact  that  the  change  of  entropy  is 
zero  in  any  case. 

If  the  cycle  is  reversible,  then  equation  (37)  may  be  used  for 
calculating  the  several  changes  of  entropy,  and  for  calculating 
the  change  for  the  entire  cycle,  giving  for  the  cycle 


(38) 


38  SECOND    LAW    OF   THERMODYNAMICS 

This  is  a  very  important  conclusion  from  the  second  law  of 
thermodynamics,  and  is  considered  to  represent  that  law.  The 
second  law  is  frequently  applied  by  using  this  equation  in  con- 
nection with  a  general  equation  or  a  characteristic  equation,  in 
a  manner  to  be  explained  later. 

Though  the  discussion  just  given  is  simple  and  complete, 
there  is  some  advantage  in  showing  that  equation  (38)  holds 
for  certain  simple  and  complex  reversible  cycles. 

Thus  for  Carnot's  cycle,  represented  by  Fig.  20,  the  increase 
of  entropy  during  isothermal  expansion  is 

!_e 


because    the    temperature    is    constant.      In     like    manner    the 
decrease  during  isothermal  compression  is 


so  that  the  change  of  entropy  for  the  cycle  is 


But  from  the  efficiency  of  the  cycle  we  have 

Q  -  Q'         T-T'  .    (y  =    F  .    Q_&  = 

Q  T  '  Q   ~"~   T  '  '   T       T'~ 

A  complex  cycle  like  that  represented  by  Fig.  24  may  be 
broken  up  into  two  simple  cycles  ABFG 
and  CDFE,  for  each  of  which  individually 
the  same  result  will  be  obtained  —  that  is, 
the  increase  of  entropy  from  A  to  B  is 
equal  to  the  decrease  from  F  to  G,  and 
the  increase  from  C  to  D  is  equal  to  the 


decrease    from  E  to  jP,  so  that    the  sum- 
mation of  changes  for  the  entire  cycle  gives  zero- 


MAXIMUM    EFFICIENCY 


39 


Fig.  25  represents  the  simplified  ideal  diagram  of  a  hot-air 
engine,  in  which  by  the  aid  of  a  regenerator  the  adiabatic  lines 
of  Carnot's  cycle  are  replaced  by 
vertical  lines  without  affecting  the 
reversibility  or  the  efficiency  of  the 
cycle.  We  may  replace  the  actual 
diagram  by  a  series  of  simple  cycles 
made  up  of  isothermals  and  adia- 
batics,  so  drawn  that  the  perimeter 
of  the  complex  cycle  includes  the 
same  area  and  corresponds  ap- 
proximately with  that  of  the 
actual  diagram.  The  summation 
for  the  complex  cycle  is  clearly 
drawing  the  adiabatic  lines  near 


FIG.  25. 

of  the  change  of  entropy 
zero,  as  before.  But  by 
enough  together  we  may 
make  the  perimeter  approach  that  of  the  actual  'diagram  as 
nearly  as  we  please,  and  we  may  therefore  conclude  that  the 
integration  for  the  changes  of  entropy  for  that  cycle  is  also  zero. 

Maximum  Efficiency.  —  In  order  that  heat  may  be  trans- 
formed into  work  with  the  greatest  efficiency,  all  the  heat  should 
be  applied  at  the  highest  practicable  temperature,  and  the  heat 
rejected  should  be  given  up  at  the  lowest  practicable  tempera- 
ture; this  condition  is  found  for  Carnot's  cycle,  which  serves 
as  the  ideal  type  to  which  we  approach  as  nearly  as  practical 
conditions  allow.  Deviations  from  the  ideal  type  are  of  two 
sorts,  (i)  commonly  a  different  and  inferior  cycle  is  chosen  as 
being  practically  more  convenient,  and  (2)  the  material  of 
which  the  working  cylinder  is  made  absor,bs  heat  at  high  tem- 
perature and  gives  out  heat  at  low  temperature,  thus  interfering 
with  the  attainment  of  the  cycle  selected. 

The  principle  just  stated  must  be  accepted  as  immediately 
evident;  but  there  may  be  an  advantage  in  giving  an  illustration. 
The  complex  cycle  of  Fig.  24  is  made  up  of  two  simple  Carnot 
cycles  ABFG  and  CDEF-,  if  two  thirds  of  the  heat  is  applied 
during  the  isothermal  expansion  AB  at  500°  C.,  and  one  third 
during  the  expansion  CD,  at  250°  C.,  and  if  all  the  heat  is  re- 


40  SECOND    LAW    OF   THERMODYNAMICS 

jected  at  20°  C.,  the  combined  efficiency  of  the  diagram  may  be 
computed  to  be 

2  500  —  20         i         250  —  20 

—  x  -*  -  +  —  x  -  =  0.50; 

3  500  +  273       3        250  +  273 

had  the  heat  been  all  applied  at  500°  C.,  the  efficiency  would 
have  been 

500  —    20 

J  -  =  0.62. 
500   +    273 

The  loss  in  this  case  from  applying  part  of  the  heat  at  lower 
temperature  is,  therefore, 

0.62  —  0.56 

- 


Non-reversible  Cycles.  —  If  a  process  or  a  cycle  is  non-rever- 
sible, then  the  change  of  entropy  cannot  be  calculated  by  equa- 
tion (37),  and  equation  (38)  will  not  hold.  The  entropy  will, 
indeed,  be  the  same  at  the  end  as  at  the  beginning  of  the  cycle, 

but  the  integration  of  -^f  for  the  cycle  will  not  give   zero.     On 

i?D 

the  contrary,  it  can  be  shown  that  the  integration  of  -^  for  the 

entire  cycle  will  give  a  negative  quantity.  Thus  let  the  non- 
reversible  engine  A  take  the  same  amount  of  heat  per  stroke  as 
the  reversible  engine  R  which  works  on  Carnot's  cycle,  but  let 
it  have  a  less  efficiency,  so  that 


where  Q/  represents  the  heat  rejected  by  the  engine  A.     Then 

6-e/  <Q-Q'  =  (T-r)  (<£'-<£)     .   .(4o) 

Suppose  now  that  T'  approaches  zero  and  that  <(>'  approaches  <f>, 
then  at  the  limit  we  shall  have 


NON-REVERSIBLE   CYCLES  41 

Integrating  for  the  entire  cycle,  we  shall  have 


where  —  N  represents  a  negative  quantity.  The  absolute 
value  of  N  will,  of  course,  depend  on  the  efficiency  of  the  non- 
reversible  engine.  If  the  efficiency  is  small  compared  with  that 
of  a  reversible  engine,  then  the  value  of  N  will  be  large.  If 
the  efficiency  approaches  that  of  a  reversible  engine,  then  N 
approaches  zero.  It  is  scarcely  necessary  to  point  out  that  N 
cannot  be  positive,  for  that  would  infer  that  the  non-reversible 
engine  had  a  greater  efficiency  than  a  reversible  engine  working 
between  the  same  temperatures. 

Some  non-reversible  operations,  like  the  flow  of  gas  through 
an  orifice,  result  in  the  development  of  kinetic  energy  of  motion. 
In  such  case  the  equation  representing  the  distribution  of  energy 
contains  a  fourth  term  K  to  represent  the  kinetic  energy,  and 
equation  (15)  becomes 

dQ  =  A  (dS  +  dl  +  dW  +  dK)      ...  (42) 

As  before  S  represents  vibration  work,  /  represents  disgregation 
work,  and  W  represents  external  work.  If  the  vibration  and 
disgregation  work  cannot  be  separated,  then  we  may  write 

dQ  =  A  (dE  +  dW  +  dK)  .....  (43) 

If  a  non-reversible  process  like  that  just  discussed  takes  place 
in  apparatus  or  appliances  that  are  made  of  non-conducting 
material,  or  if  the  action  of  the  walls  on  the  substance  contained 
can  be  neglected,  the  operation  may  properly  be  called  adiabatic  ; 
such  a  use  is  clearly  an  extension  of  the  idea  stated  on  page  32, 
and  conclusions  drawn  from  adiabatic  expansion  in  a  closed 
cylinder  cannot  be  directly  extended  to  this  new  application. 
Such  a  non-reversible  operation  is  not  likely  to  be  isoentropic, 
and  there  is  some  advantage  in  drawing  a  distinction  between 
operations  which  are  isoentropic  and  those  which  are  adiabatic. 


42  SECOND    LAW    OF    THERMODYNAMICS 

A  non-reversible  operation  in  non-conducting  receptacles  may  be 
isothermal,  or  may  be  with  constant  intrinsic  energy,  as  will 
appear  in  the  discussion  of  flow  of  air  in  pipes  on  page  380,  and 
the  discussion  of  the  steam  calorimeter,  page  191.  Any  non- 
reversible  process  is  likely  to  be  accompanied  by  an  increase  of 
entropy;  this  will  appear  in  special  cases  discussed  in  the 
chapter  on  flow  of  fluids. 

Since  the  entropy  of  a  pound  of  a  given  substance  under 
given  conditions,  reckoned  from  an  arbitrary  zero,  is  a  perfectly 
definite  numerical  quantity,  it  is  possible  to  determine  its  entropy 
for  any  series  of  conditions,  without  regard  to  the  method  of 
passing  from  one  condition  to  another.  It  is,  therefore,  always 
possible  to  represent  any  changes  of  a  fixed  weight  of  a  sub- 
stance, by  a  diagram  drawn  with  temperatures  and  entropies 
for  co-ordinates.  If  the  diagram  can  be  properly  interpreted, 
conclusions  from  it  will  be  valid.  It  is,  however,  to  be  borne  in 
mind  that  thermodynamics  is  essentially  an  analytical  mathemat- 
ical treatment ;  the  treatment,  so  far  as  it  applies  to  engineering, 
is  neither  extensive  nor  difficult.  But  the  student  is  cautioned 
not  to  consider  that  because  he  has  drawn  a  diagram  represent- 
ing a  given  operation  to  the  eye,  he  necessarily  has  a  better 
conception  of  the  operation.  If  any  operation  involves  an 
increase  (or  decrease)  of  weight  of  the  substance  operated  on, 
thermal  diagrams  are  likely  to  be  difficult  to  devise  and  liable 
to  misinterpretation. 


CHAPTER   IV. 

GENERAL  THERMODYNAMIC   METHOD. 

IN  the  three  preceding  chapters  a  discussion  has  been  given 
of  the  three  fundamental  principles  of  thermodynamics,  namely, 
(i)  the  assumption  that  the  properties  of  any  substance  can 
be  represented  by  an  equation  involving  three  variables;  (2)  the 
acceptance  of  the  conservation  of  energy;  and  (3)  the  idea  of 
Carnot's  principle.  In  the  ideal  case  each  of  these  principles 
should  be  represented  by  an  equation,  and  by  the  combination 
of  the  three  several  equations  all  the  relations  of  the  properties 
of  a  substance  should  be  brought  out  so  that  unknown  proper- 
ties may  be  computed  from  known  properties,  and  in  particular 
advantage  may  be  taken  of  opportunities  to  calculate  such  prop- 
erties as  cannot  be  readily  determined  by  direct  experiment  from 
those  which  may  be  determined  experimentally  with  precision. 

Recent  experiments  have  so  far  changed  the  condition  of 
affairs  that  there  is  less  occasion  than  formerly  for  such  a  general 
treatment.  Of  the  three  classes  of  substances  that  are  interest- 
ing to  engineers,  namely,  gases,  saturated  vapors,  and  super- 
heated vapors,  the  conditions  appear  to  be  as  follows.  For 
gases  there  are  sufficient  experimental  data  to  solve  all  problems 
without  referring  to  the  general  method,  though  the  ratio  of  the 
specific  heats  is  probably  best  determined  by  that  method.  For 
saturated  steam  there  is  one  property,  namely,  the  specific  vol- 
ume, which  is  computed  by  aid  of  the  general  method,  but  there 
are  experimental  determinations  of  volume  which  are  reliable 
though  less  extensive.  The  characteristic  equation  of  super- 
heated steam  is  now  well  determined,  and  the  specific  heat  is 
determined  with  sufficient  precision  for  engineering  purposes, 
so  that  there  is  no  difficulty  in  making  the  customary 
calculations. 

43 


44  GENERAL  THERMODYNAMIC    METHOD 

The  one  class  of  substances  for  which  the  necessary  properties 
must  be  computed  by  aid  of  the  general  method,  are  those  vola- 
tile fluids  like  ammonia  and  sulphur  dioxide,  which  are  used 
for  refrigerating  machines. 

On  the  whole,  even  with  conditions  as  stated,  it  is  desirable 
that  the  student  should  master  the  general  thermodynamic 
method,  given  in  this  chapter.  That  method  is  neither  long 
nor  hard,  and  is  so  commonly  accepted  that  students  who  have 
mastered  it  will  have  no  difficulty  in  reading  standard  works 
and  current  literature  involving  thermodynamic  discussions. 
Those  cases  remaining  where  the  general  method  or  its  equiva- 
lent must  be  used,  are  best  treated  by  that  method,  and  in  the 
case  of  volatile  fluids  can  be  treated  only  by  that  method. 

The  case  having  been  presented  as  fairly  as  possible,  dis- 
cretion may  be  left  with  the  student  or  his  instructor  whether 
he  shall  read  the  remainder  of  this  chapter  before  proceeding, 
or  whether  the  chapter  shall  be  altogether  omitted. 

The  following  method  of  combining  the  three  general  prin- 
ciples of  thermodynamics,  which  is  due  to  Lord  Kelvin,  depends 
on  the  use  of  the  expression 

S2x         &x 

Sy&z        $z$y 

as  the  basis  of  an  operation.  This  expression  is  generally  used 
as  a  criterion  to  determine  whether  a  certain  differential  is  an 
exact  differential  that  can  be  integrated  directly,  or  whether 
some  additional  relation  must  be  sought  by  aid  of  which  the 
expression  may  be  transformed  so  that  it  can  be  integrated. 

Conversely,  if  we  know,  from  the  nature  of  a  given  property 
like  intrinsic  energy,  that  it  can  be  always  calculated  for  a  given 
condition  as  represented  by  two  variables  like  temperature  and 
volume,  then  we  are  justified  in  concluding  that  the  expression 


,     , 
must  be  true  and  that  we  can  use  it  as  the  basis  of  an  operation. 


APPLICATION   OF  THE   F,IRST   LAW  45 

Now  in  laying  out  a  general  method  it  is  impossible  to  select 
any  particular  characteristic  equation,  and  for  that  reason,  if 
no  other,  the  form  of  the  integral  equation  connecting  E  with 
/  and  v  cannot  be  assigned.  But  the  fact  remains  that  the  possi- 
bility of  working  out  any  method  depends  on  the  assumption  of 
the  ultimate  possibility  of  writing  such  an  equation,  and  that 
assumption  carries  with  it  the  assumption  that  dE  is  an  exact 
differential. 

Application  of  the  First  Law.  —  The  first  general  principle 
may  be  taken  to  be  represented  by  equation  (i), 

dQ  =  cvdt  +  Idv, 

and  the  first  law  of  thermodynamics  by  equation  (16), 
dQ  =  A  (dE  +  dW)  =  A  (dE+  pdv). 

Combining  these  equations  gives 

dE  =  *  dt  +  (j  -  p)  dv; 

and  comparing  with  the  general  form, 


it  is  evident  that 


dt  + 
d/  6V 


BE       cv       ,  BE        I 
-r-  =   f  and  •£-  =  —  —  p. 
ot       A  cv       A 


Now  equation  (44)  is  an  abbreviated  way  of  writing  the 
expression  for  continued  differentiation  which  may  be  expanded 
to 

z*E        ,  BE 

JL.     IE 

Bv  Bt 


46  GENERAL  THERMODYNAMIC    METHOD 

or  replacing  the   first  partial  differential  coefficients   by  their 
equivalents, 


* 

Sv\A/~  Bt\A      f 

.......  <«> 


the  subscripts  being  written  to  avoid  possible  confusion  with 
other  partial  differential  coefficients  to  be  deduced  later. 

From  the  first  law  of  thermodynamics  and  equation   (2)  we 
have  in   like  manner 

dQ  =  A  (dE  +  pdv)  =  cpdt  +  mdp. 

Since  the  differential  dv  is  inconvenient,  we  may  replace  it  by 

Bv   ,      .   By   , 


so  that 

A   I JT?  _l_   *  _ 

Sp 


A  I  ^  Bv   ,  By       \ 

A  [  ah  +  P  TT~~  dp  +  P  -;>—  dt }  =  cndt  +  mdi). 
\  (>t>  Bt      I 


Making  use  of  the  equation 

*BE    *  BE 


glves 


Bp   '       Bt 
B 


_  L         v     L 

'  A  \Bpt    '  Bt"  p  BpBt      A  \Bt/P      p  BtBp 


APPLICATION    OF    THE    SECOND    LAW 


47 


But  the  assumption  of  a  characteristic  equation  connecting 
,  v,  and  t  carries  with  it  the  assumption  that 


so  that 


( 

\ 


Bm 

tt 


Again,  from  equation  (3)  we  may  have 

dQ  =  A  (dE  +  pdv)  =  ndp  +  odv. 


......  (47) 

or,  making  use  of 


L  f^L\       L  /M 
A  \SvJp      A\B)v 


Bp)v 


Application  of  the  Second  Law.  —  The  second  law  of  thermo- 
dynamics can  be  expressed  by  equation  (38),  page  37, 


which  makes  -     or  d<j>  an  exact  differential,  so  that  we  may  write 


To  prepare  equation  (i)  for  this  transformation,  we  may  write 


48  GENERAL   THERMODYNAMIC    METHOD 

so  that  the  preceding  equation  gives 


T2 

/SA        /Sr.\        I 
or 


©.-(a- 1 <«> 

Performing  a  like  operation  on  equation  (2)  we  have 


Again,  from  equation  (3)  we  have 

dO       n    ,          o  , 
T  =.T    p  +  T 

S   /£ 
T- 

^-]   -n~      T  l^-J  -, 


S 


First  and  Second  Laws  Combined.  —  The  result  of  applying 
both  the  first  and  the  second  laws  of    thermodynamics  to  the 


ALTERNATIVE    METHOD  49 

equations  (i),  (2),  and  (3)  may  be  obtained  by  combining  the 
equations  resulting  from  the  application  of  the  laws  separately. 
Thus  equations   (45)  and   (49)  give 

*p        i    I 

Tt=-AT     *     .......  (52) 

Equations  (46)  and  (50)  give 


dt  A  T 

And  equations  (48)  and  (51)  give 

«/  8A 

Jp"nW  .....   (54) 

It  is  convenient  to  transform  this  last  equation  by  taking 
values  of  n  and  o  from  page  12,  yielding 

<>-<'  =  ATw*  ......  (S5) 

&v  &p 

The  equations  deduced  in  this  chapter  show  the  necessary 
relations  among  the  thermal  capacities  if  the  laws  of  thermo- 
dynamics are  accepted.  Some  of  them,  or  equations  deduced 
from  them,  have  been  used  by  writers  on  thermodynamics  to 
establish  relations  or  compute  properties  that  cannot  be  readily 
obtained  by  direct  experiments. 

For  the  student  familiarity  with  the  processes  is  of  more 
importance  than  any  of  the  results. 

Alternative  Method.  —  Some  writers  on  thermodynamics  re- 
serve the  discussion  of  temperature  until  they  are  ready  to 
define  or  assume  an  absolute  scale  independent  of  any  substance 
and  depending  only  on  the  fundamental  units  of  length  and 
weight.  Of  the  three  general  equations  (i),  (2),  and  (3)  they 
use  at  first  only  the  latter: 

dQ  =  ndp  -f  odv. 


50  GENERAL  THERMODYNAMIC    METHOD 

Now  from  equation  (16),  representing  the  first  law  of  thermo- 
dynamics, 

dQ  =  A  (dE  +  pdv), 

it  is  evident  that  dQ  is  not  an  exact  differential,  since  the  equa- 
tion cannot  be  integrated  directly.  The  fact  that  in  certain 
cases  p  may  be  expressed  as  a  function  of  v,  and  the  integral 
for  external  work  can  be  deduced,  does  not  affect  this  general 
statement.  Suppose  that  there  is  some  integrating  factor, 

which  may  be  represented  by  — ,  so  that 

o 

dQ       n    ,         o  , 

s~sdp  +  sdv 

may  be  integrated  directly;  we  may  then  consider  that  we  have 
a  series  of  thermal  lines  represented  by  making 

-  =  const.,  •—  =  const.,  —  =  const.,  etc. 

These  lines  with  a  series  of  adiabatic  lines  represented  by 
<j>  =  const.,  (j>f  =  const.,  <£"  =  const.,  etc., 

allow  us  to  draw  a  simple  cycle  of  operations  represented  by  Fig. 
2$a,  in  which  AB  and  CD  are  represented  by  the  equations 


j  =    C,   and  J;  =  C', 


while  AD  and  BC  are  adiabatics.     The  effi- 
JL    ciency   of   a   reversible   engine   receiving   the 


FIG.  aSa.  ^eat  Q  during  the  operation  AB,  and  reject- 

ing the  heat  Qf  during  the  operation  CD,  will  be 


But  —  is  an  exact  differential,  and  depends  on  the  state  of 
o 


ZEUNER'S    EQUATIONS  51 

the  substance  only,  and  consequently  is  the  same  at  the  end  as 
at  the  beginning  of  the  cycle,  so  that  for  the  entire  cycle 


Now  during  the  operations  represented  by  the  adiabatics  AD 
and  EC  no  heat  is  transmitted,  and  during  the  operations  rep- 

resented by  the  lines  AB  and  CD,  -  is  constant;  consequently 

o 

the  integration  of  the  above  equation  for  the  cycle  gives 

Q     Q' 

—  —  **—  =  o. 

S       S' 


that  is,  the  efficiency  of  an  engine  working  on  such  a  cycle  depends 
on  S  and  S',  and  on  nothing  else. 

Zeuner's  Equations.  —  A  special  form  of  thermodynamic 
equations  has  been  developed  by  Zeuner  and  through  his  influ- 
ence has  been  impressed  to  a  large  extent  on  German  writings. 
These  equations  can  be  deduced  from  those  already  given  in 
the  following  manner. 

From  the  application  of  the  first  law  of  thermodynamics  to 
equation  (3)  we  have  equation  (47),  page  47, 


°-  p]dv. 
i  / 


Now 

JK       SE^    ,  *E  j 

dE-'Tpd*+hdv' 

so  that 

n        BE  o        8E 

A="  *p'         A="  8^ 

These  properties  Zeuner  writes 


52  GENERAL  THERMODYNAMIC    METHOD 

Solving  equation  (54)  first  for  o  and  then  for  w, 


0  = 


—  n  = 


Bp 


A 

Sv 
In  equation  (3) 

dQ  =  ndp  +  odv, 

we  may  substitute  the  above  values  successively  giving 


.'.  dQ  =       (ndt  +  ATdv 


because  dt  =  ^ —  dp  +  T— 

op  ov 

And  also 


_ 

&V 

.:dQ  =  ^(odt  —  ATdp\- 
"K 

Replacing  o  and  n  by  their  values  in  terms  of  X  and  F, 
dQ  =A  (Xdp  +  Ydv), 


ZEUNER'S    EQUATIONS  53 

In  these  equations  a  is  the  coefficient  of  dilatation,  or  -  +  /   is 

a. 

equal  to  T,  and 


If  this  derivation  of  Zeuner's  equations  is  borne  in  mind,  the 
treatment  of  thermodynamics  by  many  German  writers  may  be 
readily  recognized  to  be  only  a  variant  on  that  developed  by 
Clausius  and  Kelvin. 


CHAPTER   V. 

PERFECT   GASES. 

THE  characteristic  equation  for  a  perfect  gas  is  derived  from 
a  combination  of  the  laws  of  Boyle  and  Gay-Lussac,  which 
may  be  stated  as  follows: 

Boyle's  Law.  —  When  a  given  weight  of  a  perfect  gas  is  com- 
pressed (or  expanded)  at  a  constant  temperature  the  product 
of  the  pressure  and  the  volume  is  a  constant.  This  law  is  nearly 
true  at  ordinary  temperatures  and  pressures  for  such  gases  as 
oxygen,  hydrogen,  and  nitrogen.  Gases  which  are  readily 
liquefied  by  pressure  at  ordinary  temperatures,  such  as  ammonia 
and  carbonic  acid,  show  a  notable  deviation  from  this  law.  The 
law  may  be  expressed  by  the  equation 

PV  =  Pi»i (5°) 

in  which  p^  and  v^  are  the  initial  pressure  and  volume;  p  is  any 
pressure  and  v  is  the  corresponding  volume. 

Gay-Lussac's  Law.  —  It  was  found  by  Gay-Lussac  that  any 
volume  of  gas  at  freezing-point  increases  about  0.003665  of  its 
volume  for  each  degree  rise  of  temperature.  Gases  which  are 
easily  liquefied  deviate  from  this  law  as  well  as  from  Boyle's 
law.  In  the  deduction  of  this  law  temperatures  were  measured 
on  or  referred  to  the  air-thermometer,  and  the  law  therefore 
asserts  that  the  expansibility  or  the  coefficient  of  dilatation  of 
perfect  gases  is  the  same  as  that  of  air.  Gay-Lussac 's  law  may 
be  expressed  by  the  equation 

v  =  v0  (i  +  at) (57) 

in  which  v0  is  the  original  volume  at  freezing-point,  a  is  the 
coefficient  of  dilatation  or  the  increase  of  volume  for  one  degree 
rise  of  temperature,  and  v  is  the  volume  corresponding  to  the 
temperature  /  measured  from  freezing-point. 

54 


CHARACTERISTIC    EQUATION  55 

Characteristic    Equation.  —  From    equation     (57)    we    may 
calculate  any  special  volume,  such  as  vlt  getting 

vt  =  v0  (i  +  at). 

Assuming  that  pt  in  equation  (56)  is  the  normal  pressure  of 
the  atmosphere  pQ,  and  substituting  the  value  just  found  for  vlt 
we  have  for  the  combination  of  the  laws  of  Boyle  and  Gay- 
Lussac 

pv  =  pQv0  (i  +  at)  =  pQv0a  (^  +  tj    .     .     .     .   (58) 

If  it  be  assumed  that  a  gas  contracts  a  part  of  its  volume  at 
freezing-point    for  each   degree  of  temperature  below   freezing 

then  the  absolute  zero  of  the  air-thermometer  will  be  —  degrees 
below  freezing,  and 


a 

may  be  replaced  by  T,  the  absolute  temperature  by  the  air- 
thermometer. 

The   usual   form   of   the   characteristic   equation   for   perfect 
gases  may  be  derived  from  equation   (58)  by  substituting  T0, 

the  absolute  temperature  of  freezing-point,  for  —  ,  giving 


•*•  0 


......   (59) 

where  R  is  a  constant  representing  the  quantity 


For  solution  of  examples  it  is  more  convenient  to  write  equa- 
tion (59)  in  the  form 

.......  (60) 


56  PERFECT    GASES 

Absolute  Temperature.  —  Recent  investigations  of  the  prop- 
erties of  hydrogen  by  Professor  Callender  *  indicate  that  the 
absolute  zero  is  273°.!  C.  below  freezing-point.  This  does 
not  differ  much  from  taking  a  =  0.003665  as  given  by  Regnault, 
for  which  the  reciprocal  is  272.8.  In  this  work  we  shall  take 
for  the  absolute  temperature 

T  =  t  +  273°  centigrade  scale. 
T  =  /  +  459°.$  Fahrenheit  scale. 

These  figures  are  convenient  and  sufficiently  exact. 

Relation  of  French  and  English  Units.  —  For  the  purpose  of 
conversion  of  units  from  the  metric  system  (or  vice  versa)  the 
following  values  may  be  used: 

one  metre       =  39.37  inches, 
one  kilogram  =  2.2046  pounds. 

Specific  Pressure.  —  The  normal  pressure  of  the  atmosphere 
is  assumed  to  be  equivalent  to  that  of  a  column  of  mercury, 
760  mm.  high  at  freezing-point.  Now  Regnault  t  gives  for 
the  weight  of  a  litre,  or  one  cubic  decimetre,  of  mercury  13.5959 
kilograms;  consequently  the  specific  pressure  of  the  atmosphere 
under  normal  conditions  is 

p0  =  10,333  kilograms  per  square  metre. 

Using  the  conversion  units  given  above  for  reducing  this 
specific  pressure  to  the  English  system  of  units  gives 

po  =  2116.32  pounds  per  square  foot, 

which  corresponds  to 

14.697  pounds  per  square  inch, 
or  to 

29.921  inches  of  mercury. 

It  is  customary  and  sufficient  to  use  for  the  pressure  of  the 
atmosphere  14.7  pounds  to  the  square  inch. 

*  Phil.  Mag.,  Jan.,  1903. 

t  Mtmoires  de  rinstUut  de  France,  vol.  xxL 


SPECIFIC   VOLUMES  57 

Specific  Volumes  of  Gases.  —  From  recent  determinations  of 
densities  of  gases  by  Leduc,  Morley,  and  Raleigh  it  appears  that 
the  most  probable  values  of  the  specific  volume  of  the  commoner 
gases  are 

VOLUMES   IN   CUBIC   METRES   OF   ONE   KILOGRAM. 

Atmospheric  air  .............  0.7733 

Nitrogen  ................  °-7955 

Oxygen     ................  0.6996 

Hydrogen     .............    .    .  11.123 

The  corresponding  quantities  for  English  units  are  given  in 
the  next  table: 

VOLUMES   IN   CUBIC   FEET   OF  ONE   POUND. 

Atmospheric  air    .    .    t    ........    c  1  2  .  39 

Nitrogen     ..........    .    c  .    .    .    .  12.74 

Oxygen   ................  11.21 

Hydrogen   ...............  178.2 

To  these  may  be  added  the  value  for  carbon  dioxide,  0.506 
cubic  metre  per  kilogram  or  8.10  cubic  feet  per  pound;  but 
as  the  critical  temperature  for  this  substance  is  about  31°  C.,  or 
88°  F.,  calculations  by  the  equations  for  gases  are  liable  to  be 
affected  by  large  errors. 

Value  of  R.  —  The  constant  R  which  appears  in  the  usual 
form  of  the  characteristic  equation  for  a  gas  represents  the 
expression 


The  values  for  R  corresponding  to  the  French  and  the  English 
system  of  units  may  be  calculated  as  follows:   - 

French  units,  R  =  IO333  *  0.7733  _  2^    .     .   (6j) 

English  units,  R  =  2"6'3  X  "^    _  53.35    .     .   (6a) 
49I-S 

Value  of  R  for  other  gases  may  be  calculated  in  a  like  manner. 


58  PERFECT    GASES 

Solution  of  Problems.  —  Many  problems  involving  the  proper- 
ties of  air  or  other  gases  may  be  solved  by  the  characteristic 
equation 

pv  =  RT, 

or  by  the  equivalent  equation 


which  for  general  use  is  the  more  convenient. 

In  the  first  of  these  two  equations  the  specific  pressure  and 
volume  to  be  used  for  English  measures  are  pounds  per  square 
foot,  and  the  volume  in  cubic  feet  of  one  pound. 

For  example,  let  it  be  required  to  find  the  volume  of  3  pounds 
of  air  at  60  pounds  gauge-pressure  and  at  100°  F.  Assuming  a 
barometric  pressure  of  14.7  pounds  per  square  inch, 


„  =  53.35  (459-5  = 

(14.7  +  60)  144 

is  the  volume  of  i  pound  of  air  under  the  given  conditions,  and 
3  pounds  will  have  a  volume  of 

3  X  2.774  =  8.322  cubic  feet. 

The  second  equation  has  the  advantage  that  any  units  may 
be  used,  and  that  it  need  not  be  restricted  to  one  unit  of  weight. 

For  example,  let  the  volume  of  a  given  weight  of  gas,  at  100°  C. 
and  at  atmospheric  pressure,  be  2  cubic  yards;  required  the 
volume  at  200°  C.  and  at  10  atmospheres.  Here 

10  v  _  1X2 
473  "      373 

473  X  2  ,       ,  .  . 

v  _  J±L£  -  _  0.2C26  cubic  yards. 
10  X  373 

Specific  Heat  at  Constant  Pressure.  —  The  specific  heat  for 
true  gases  is  very  nearly  constant,  and  may  be  considered  to  be 


APPLICATION    OF   LAWS    OF   THERMODYNAMICS  59 

so  for  thermodynamic  equations.  Regnault  gives  for  the  mean 
values  for  specific  heat  at  constant  pressure  the  following  results : 

Atmospheric  air 0.2375 

Nitrogen 0.2438 

Oxygen 0.2175 

Hydrogen 3-409 

Ratio  of  the  Specific  Heats.  —  By  a  special  experiment  on 
the  adiabatic  expansion  of  air,  Rontgen*  determined  for  the 
ratio  of  the  specific  heats  of  air,  at  constant  pressure  and  at 
constant  volume,  ^ 

K  =  c*  =  1.405. 

cv 

This  value  agrees  well  with  a  computation  to  follow,  which 
depends  on  the  application  of  the  laws  of  thermodynamics  to  a 
perfect  gas,  and  also  with  a  determination  from  the  theory  of 
gases  by  Lovef  that  the  ratio  for  air  should  be  1.403.  If  the 
given  value  for  this  ratio  be  accepted  the  remainder  of  the  work 
in  this  chapter  follows  without  any  reference  to  the  laws  of 
thermodynamics. 

Application  of  the  Laws  of  Thermodynamics.  —  The  preced- 
ing statements  concerning  the  specific  heats  of  perfect  gases 
and  their  ratio  would  be  satisfactory  were  it  definitely  determined 
by  experiment  that  the  specific  heat  at  constant  volume  is  as 
nearly  constant  as  is  the  specific  heat  at  constant  pressure. 
None  of  the  experimental  determinations  (not  even  that  by  Joly  J) 
can  be  considered  as  satisfactory  as  those  for  the  specific  heat 
at  constant  pressure;  consequently  there  is  considerable  impor- 
tance to  be  attached  to  the  application  of  the  laws  of  thermo- 
dynamics to  the  characteristic  equation  for  a  perfect  gas,  and, 
moreover,  this  application  furnishes  one  of  the  most  satisfactory 
determinations  of  the  ratio  of  the  specific  heats. 

*  Poggendorff's  Annalen,  vol.  cxlviii,  p.  580. 

t  Phil.  Mag.,  July,  1899. 

J  Proc.  Royal  Soc.,  vol.  xli,  p.  352,  1886. 


60  PERFECT   GASES 

It  is  convenient  at  this  place  to  make  the  application  of  the 
laws  of  thermodynamics  by  aid  of  equation  (55),  page  49. 


.     ......  (63) 

$v  &p 
From  the  equation 


pv  =  RT, 
we  have  &  St 


=  AR      ......  (64) 


This  equation  shows  conclusively  that  if  the  characteristic 
equation  is  accepted  the  differences  of  the  specific  heats  must  be 
considered  to  be  constant,  and  if  one  is  treated  as  constant  so 
also  must  the  other.  Conversely,  the  assumption  of  constant 
specific  heats  for  any  substance  is  in  effect  the  assumption  of 
the  characteristic  equation  for  a  perfect  gas. 

The  solution  of  equation  (64)  for  the  ratio  of  the  specific 
heats  gives  r 

cP 

= 


K= 


10333    X  0.7733 


426.9  X  273  X  0.2375 

For  those  who  have  not  read  Chapter  IV,  the  following  deriva- 
tion of  equation  (64)  may  be  interesting.     In  Fig.  26  let  ab  repre- 
sent the  change  of  volume  at  constant  pressure  due 
to  the  addition  of  heat  cp&t  where  A/  is  the  increase 
of  temperature  ;  and  let  cb  represent  the  change  of 
v  pressure  due  to  the  addition  of  heat  cvA/;  if  ac  is 


FIG.  26.  an  isothermal,  the  latter  change  of  temperature  will 
be  equal  to  the  former,  but  the  heat  applied  will  be  less  on  account 
of  the  external  work  p&u  (approximtely).  Consequently, 

r\ 

cp  —  cv  =  Ap      =  AR, 


ISOTHERMAL   LINE  6l 

the  last  transformation  making  use  of  the  partial  derivative 

S/  "  p' 

Thermal  Capacities.  —  The  values  of  the  several  thermal 
capacities  for  a  perfect  gas  were  derived  on  page  12  and  may  be 
written 

-  R  (CP      c*)  -  v  (CP      c<>)    *  ( 

v   .  .  T  .  ,  ,,  . 

™  =   —  •£  (Cp  —  O   =  —  -  (Cp  —  O     .       .    (67) 

»  =  r<=r' (68) 

—£*-?*   •  • w 

the  transformations  in  equations  (66)  and  (67)  being  made  by 
aid  of  the  characteristic  equation. 

General  Equations.  —  To  deduce  the  general  equations  for 
gases  from  equations  (i),  (2),  and  (3),  it  is  only  necessary  to 
replace  the  letters  /,  m,  n,  and  o  by  their  values  just  obtained, 
giving 

T 

dQ  =  cvdt  +  (cp  —  cv)  —  dv (70) 

v 

J 

T  T 

dQ  =  cv  -dp  +  cp-  dv (72) 

p  v 

Isothermal  Line.  —  The  equation  to  the  isothermal  line  for 
a  gas  is  obtained  by  making  T  a  constant  in  the  characteristic 
equation,  so  that 


or 

pv  =  pLvl       .     .     .     .     .     .  (73) 

This  equation  will  be  recognized  as  the  expression  of  Boyle's 
law.     It  is,  of  course,  the  equation  to  an  equilateral  hyperbola. 


62  PERFECT   GASES 

To  obtain  the  external  work  during  an  isothermal  expansion 
we  may  substitute  for  p  in  the  expression 


W 


-/#*  , 


from  the  equation  to  the  isothermal  line  just  stated,  using  for 
limits  the  final  and  initial  volumes,  v2  and  vv 

"»....  (74) 

If  the  problem  in  any  case  calls  for  the  external  work  of  one 
unit  of  weight  of  a  gas,  then  v^  and  v2  must  be  the  initial  and 
final  specific  volumes;  but  in  many  cases  the  initial  and  final 
volumes  are  given  without  any  reference  to  a  weight,  and  it  is 
then  sufficient  to  find  the  external  work  for  the  given  expansion 
from  the  initial  to  the  final  volume  without  considering  whether 
or  not  they  are  specific  volumes. 

The  pressures  must  always  be  specific  pressures ;  in  the  English 
system  the  pressures  must  be  expressed  in  pounds  on  the  square 
foot  before  using  them  in  the  equation  for  external  work,  or,  for 
that  matter,  in  any  thermodynamic  equation. 

For  example,  the  specific  volume  of  air  at  freezing-point  and 
at  14.7  pounds  pressure  per  square  inch  is  about  12.4  cubic  feet; 
at  the  same  temperature  and  at  29.4  pounds  per  square  inch  the 
specific  volume  is  6.2  cubic  feet.  The  external  work  during 
an  isothermal  expansion  of  one  pound  of  air  from  6.2  to  12.4 
cubic  feet  is 


=  29.4  X  144  X  6.2  loge  —-*  =18,190  foot-pounds. 

For  example,  the  external  work  of  isothermal  expansion  from 
3  cubic  feet  and  60  pounds  pressure  by  the  gauge  to  a  volume 
of  7  cubic  feet  is 

W  =  (60  +  14.7)  144  X  3  logg-2-  =  27,340  foot-pounds. 

o 


ISOENERGIC    LINE  63 

In  both  problems  the  pressure  per  square  inch  is  multiplied 
by  144  to  reduce  it  to  the  square  foot.  In  the  first  problem  the 
pressures  are  absolute,  that  is,  they  are  measured  from  zero 
pressure;  in  the  second  problem  the  pressure  by  the  gauge  is 
60  pounds  above  the  pressure  of  the  atmosphere,  which  is  here 
assumed  to  be  14.7  pounds  per  square  inch,  and  is  added  to 
give  the  absolute  pressure.  In  careful  experimental  work  the 
pressure  of  the  atmosphere  is  measured  by  a  barometer  and  is 
added  to  the  gauge-pressure. 

Isoenergic  Line.  —  The  isothermal  line  for  a  perfect  gas  is 
also  the  isoenergic  line,  a  fact  that  may  be  proved  as  follows: 
The  heat  applied  during  an  isothermal  expansion  may  be  cal- 
culated by  making  T  a  constant  in  equation  (70)  and  then 
integrating;  thus: 

r»  /77 1  r; 

f-  =  (',  ~  c.)  T,  log,  J 

or,  substituting  for  cp  —  cv  from  equation  (64), 

Q  =  ART,  \og,^  =  AplVl  loge^     .    .    .   (75) 

Vl  Vl 

A  comparison  of  equation  (75)  with  equation  (74)  shows 
that  the  heat  applied  during  an  isothermal  expansion  is  equiv- 
alent to  the  external  work,  or  we  may  say  that  all  the  heat  applied 
is  changed  into  external  work,  so  that  the  intrinsic  energy  is  not 
changed.  This  conclusion  is  based  on  the  assumption  that 
the  properties  are  accurately  represented  by  the  characteristic 
equation  and  that  the  specific  heats  are  constant.  As  both 
assumptions  are  approximate  so  also  is  the  conclusion,  as  will 
appear  in  the  discussion  of  flow  through  a  porous  plug. 

An  interesting  corollary  of  the  discussion  just  given  is  that 
an  infinite  isothermal  expansion  gives  an  infinite  amount  of 
work.  Thus  the  area  contained  between  the 
axis  OF  (Pig.  27),  the  ordinate  ab,  and  the 
isothermal  line  aa  extended  without  limit  is 

W  =  p0v0  log,  —  =  oo.  ^^^^ 

^0  FIG.  ,7. 


64  PERFECT   GASES 

This  may  also  be  seen  from  the  consideration  that  if  heat  be 
continually  applied,  and  all  changed  into  work,  there  will  be  a 
limitless  supply  of  work. 

Adiabatic  Lines.  —  During  an  adiabatic  change  —  for  exam- 
ple, the  expansion  of  a  gas  in  a  non-conducting  cylinder  —  heat 
is  not  communicated  to,  nor  abstracted  from,  the  gas;  conse- 
quently dQ  in  equations  (70),  (71),  and  (72)  becomes  zero. 

From  equation   (72) 

T  T 

o  =  dQ  =  cv  —  dp  +  cp  —  dv\ 
p  v 

Cgdv  _     _  dp 
cv  v  ~          p  ' 


The  ratio  -  of  the  specific  heats  may  be  represented  by  *,  and 

cv 

the  above  equation  may  be  written 


(-)"= 

w 


/.    v*p  =  vfpt  =  const  .......   (77) 

This  is  the  adiabatic  equation  for  a  perfect  gas  which  is  most 
frequently  used.  If  adiabatic  equations  involving  other  varia- 
bles, such  as  v^  and  7\,  are  desired,  they  may  be  derived  from 
equation  (76)  by  aid  of  the  characteristic  equation,  which  for 
this  purpose  may  be  written 


so   that 


(79) 


ADIABATIC    LINES 


Or   equations    (78)   and    (79)   may   be   deduced  directly   from 
equation  (70)  as  equations  (76)  and  (77)  were  from  equation 

(72). 
In  like  manner  we  may  deduce  from  equation  (71) 

Tp~=  T^~  .......  (80) 

or  we  may  derive  it  from  equation  (76). 
To  find  the  external  work  the  equation 

W  =  Cpdv 

may  be  used  after  substituting  for  p  from  equation  (77) 


K  —    I 


In   Fig.  28  the  area   between  the  axis   OF,    P 
the  ordinate  ba,  and  the  adiabatic  line  aa  ex- 
tended without  limit,  becomes 


K—  I 


FIG.  28. 


and  not  infinity,  as  is  the  case  with  the  isothermal  line. 

Here,  as  with  the  calculation  of  external  work  during  iso- 
thermal expansion,  specific  volumes  should  be  used  when  the 
problem  involves  a  unit  of  weight;  but  work  may  be  calculated 
for  any  given  initial  and  final  volumes  without  considering 
whether  they  are  specific  volumes  or  not.  The  pressures  are 
always  pounds  on  the  square  foot  for  the  English  system. 

For  example,  the  external  work  of  adiabatic  expansion  from 
3  cubic  feet  and  60  pounds  pressure  by  the  gauge  to  the  volume 
of  7  cubic  feet  is 


66  PERFECT   GASES 

which  is  considerably  less  than  the  work  for  the  corresponding 
isothermal  expansion. 

Attention  should  be  called  to  the  fact  that  calculations  by  this 
method  are  subject  to  a  considerable  error  from  the  fact  that 
the  denominator  of  the  coefficient  contains  the  term  K  —  i  equal 
to  0.405  ;  if  it  be  admitted  that  the  last  figure  is  uncertain  to  the 
extent  of  two  units,  the  error  of  calculation  becomes  half  a  per 
cent. 

Intrinsic  Energy.  —  Since  external  work  during  an  adiabatic 
expansion  is  done  at  the  expense  of  the  intrinsic  energy,  the  work 
obtainable  by  an  infinite  expansion  cannot  be  greater  than  the 
intrinsic  energy.  If  it  be  admitted  that  such  an  expansion 
changes  all  of  the  intrinsic  energy  into  external  work  we  shall 
have 


JE,  =  Wl  =  ......  (82) 

'_      .  ?* 

which  gives  a  ready  way  of  calculating  intrinsic  energy.  In 
practice  we  always  deal  with  differences  of  intrinsic  energy,  so 
that  even  if  there  be  a  residual  intrinsic  energy  after  an  infinite 
adiabatic  expansion  the  error  of  our  method  will  be  eliminated 
from  an  equation  having  the  form 


....  .(83) 

Exponential  Equation.  —  The  expansions  and  compressions 
of  air  and  other  gases  in  practice  are  seldom  exactly  isothermal  or 
adiabatic;  more  commonly  an  actual  operation  is  intermediate 
between  the  two.  It  is  convenient  and  usually  sufficient  to 
represent  such  expansions  by  an  exponential  equation, 


(84) 


in  which  n  has  a  value  between  unity  and  1.405.  The  form  of 
integration  for  external  work  is  the  same  as  for  that  of  adiabatic 
expansion,  and  the  amount  of  external  work  is  intermediate 
between  that  for  adiabatic  and  that  for  isothermal  expansion. 


THE 

UNIVERSITY 

OF 


ENTROPY 


67 


Change  of  temperature  during  such  an  expansion  may  be 
calculated  by  the  equations 

Tvn~l  =  T.v?-1     .......   (85) 

l-n  1-n 

Tp~  =  Ttp,~    .......   (86) 

which  may  be  deduced  from  equation  (84)  by  aid  of  the  char- 

acteristic equation  D~ 

pv  =  Kl 

as  equation  (79)  is  deduced  from  equation  (76). 

If  it  is  desired  to  find  the  exponent  of  an  equation  representing 
a  curve  passing  through  two  points,  as  al  and  a2    ' 
(Fig.  29),  we  may  proceed  by  taking  logarithms 
of  both  sides  of  the  equation 


so  that 


n  log  vl  +log  pl  =  n  log  v2  +  log  #2, 
n  =  log  />,  —  log  p2 

log  772  "    log  VL 


F'G- 


(87) 


For  example,  the  exponent  of  an  equation  to  a  curve  passing 
through  the  points 

p,  =  74.7,     vt  =  3,     and  p2  =  30,     v2  =  7, 

is  n=  Iop4.7  -log  30  =I>IQ4> 

log  7  —  log  3 

It  should  be  noted  that  as  n  approaches  unity  the  probable 
error  of  calculation  of  external  work  is  liable  to  be  very  large. 
Entropy.  —  For  any  reversible  process 


consequently  from  equations  (70),  (71),  and  (72)  we  have 

,  ,  dt 

d<t>  -  cv  - 

,  .  dt 


.  dv 
(cp  -  cv)  — 


,, 
d<t>  =  c 


.dp 

-    +  (cv  —  cp)  -f-> 
T  p 

dp  dv 

=       --          — 


68  PERFECT   GASES 

and,  integrating  between  limits, 


(cp  -  cv)  log.  -2     .     .  (88) 


,-*,-  c,  log,  |L  +  (<v  -  e.)  log,          .     .   (89) 


<t>2~  <t>L  =   Cv  k)ge^     +    Cp  loge    ~2       .       .       .       .     (90) 
Pi  Vl 


which  give  ready  means  of  calculating  changes  of  entropy. 
These  equations  give  the  entropy  changes  per  pound,  and  are  to 
be  multiplied  by  the  weight  in  pounds  to  give  the  change  for 
the  actual  conditions. 

For  example,  the  change  of  entropy  in  passing  from  the  pres- 
sure of  74.7  pounds  absolute  per  square  inch  and  the  volume 
of  3  cubic  feet  to  the  pressure  of  30  pounds  absolute  and  the 
volume  of  7  cubic  feet  is 

£2  —  01  =  °'2375    loge    -^-    +   0.2375  loge  -  =  0.0454. 
*  i     0  /   •*  I  O 

Since  the  pressures  form  the  numerator  and  denominator  of 
a  fraction,  there  is  no  necessity  to  reduce  them  to  the  square 
foot.  In  this  problem  the  pressures  and  volumes  are  taken  at 
random;  they  correspond  to  a  temperature  of  146°  F.,  at  the 
initial  condition.  As  has  already  been  said,  there  is  seldom 
occasion  in  practice  for  using  the  entropy  of  a  gas. 

Comparison  of  the  Air-Thermometer  with  the  Absolute  Scale. 
—  In  connection  with  the  isodynamic  line  it  was  shown  that  the 
intrinsic  energy  is  a  function  of  the  temperature  only.  This 
conclusion  is  deduced  from  the  characteristic  equation  on  the 
assumption  that  the  scale  of  the  air-thermometer  coincides  with 
the  thermodynamic  scale,  and  it  affords  a  delicate  method  of 
testing  the  truth  of  the  characteristic  equation,  and  of  comparing 
the  two  scales. 


COMPARISON  OF   THE   AIR  THERMOMETER  69 

The  most  complete  experiments  for  this  purpose  were  made 
by  Joule  and  Lord  Kelvin,  who  forced  air  slowly  through  a  porous 
plug  in  a  tube  in  such  a  manner  that  no  heat  was  transmitted 
to  or  from  the  air  during  the  process.  Also  the  velocity  both 
before  and  beyond  the  plug  was  so  small  that  the  work  due  to 
the  change  of  velocity  could  be  disregarded.  All  the  work  that 
would  be  developed  in  free  expansion  from  the  higher  to  the 
lower  pressure  was  used  in  overcoming  the  resistance  of  friction 
in  the  plug,  and  so  converted  into  heat,  and  as  none  of  this  heat 
escaped  it  was  retained  by  the  air  itself,  the  plug  remaining  at  a 
constant  temperature.  It  therefore  appears  that  the  intrinsic 
energy  remained  the  same,  and  that  a  change  of  temperature 
indicated  a  deviation  from  the  assumptions  of  the  theory  of 
perfect  gases. 

In  the  discussion  of  results  given  by  Joule  and  Lord  Kelvin* 
in  1854  they  gave  for  the  absolute  temperature  of  freezing-point 
273°-7  C.  As  the  result  of  later  experiments  f  they  stated  that 
the  cooling  for  a  difference  of  pressure  of  100  inches  of  mercury 
was  represented  on  the  centigrade  scale  by 


°'°92  V   T   I 


From  these  experiments  and  from  other  considerations  con- 
cerning the  constant- volume  hydrogen  thermometer,  Professor 
Callendar  has  determined  that  the  most  probable  value  for  the 
absolute  temperature  of  freezing-point  is  273°.!  C.,  as  already 
given,  and  gives  a  table  of  corrections  to  the  hydrogen  ther- 
mometer to  obtain  temperatures  on  the  absolute  scale.  As 
the  correction  at  any  temperature  between  —  200°  and  +  450° 
C.  is  not  more  than  litf  of  a  degree  this  is  interesting  mainly 
to  physicists.  The  corrections  for  the  air-thermometer  at  con- 
stant pressure  are  somewhat  larger,  but  approach  A  of  a  degree 
only  at  300°  C. 

*  Phil.  Trans,  vol.  cxliv,  p.  349. 
t  Ibid.  vol.  clii,  p.  579. 


7o 


PERFECT   GASES 


Deviation  from  Boyle's  Law.  —  Early  experiments  on  the 
permanent  gases  (as  they  were  then  known)  indicated  that 
there  were  small  deviations  evident  to  a  physicist,  but  not  of 
importance  to  engineers;  but  now  that  air  is  compressed  to 
pressures  as  high  as  2500  pounds  per  square  inch,  it  becomes 
necessary  to  take  account  of  such  deviations  in  engineering 
practice. 

Perhaps  the  best  conception  of  this  subject,  and  of  the  four 
recognized  states  of  fluids,  can  be  had  from  a  consideration  of 
Andrews'  *  experiments,  which  for  the  present  purpose  are  con- 
veniently represented  by  his  isothermal  curves,  which  are  repro- 
duced in  Fig.  2ga,  together  with  the  curves  for  air.  The  latter 
are  approximate  hyperbolae  referred  to  the  proper  axes,  that 
for  zero  pressure  being  nearly  the  whole  height  of  the  diagram 
below  the  figure  as  it  is  drawn.  At  48°. i  C.,  the  isothermal  for 
carbonic  acid  shows  a  marked  deviation  from  the  hyperbola,  as 
may  be  seen  by  comparison  with  the  curves  for  air,  or  better 
from  the  fact  that  a  rectangular  hyperbola  through  P  will  pass 
through  Q.  On  the  other  hand,  the  isothermal  for  13°.!  resem- 
bles that  for  steam,  which  is  commonly  known  as  a  saturated 
vapor  whose  pressure  is  constant  at  constant 
temperature;  the  horizontal  part  of  this  line 
represents  a  mixture  of  liquid  and  vapor 
which  at  the  left  runs  into  the  liquid  curve, 
and  as  liquid  carbonic  acid  has  considerable 
compressibility,  this  curve  becomes  a  straight 
line  with  an  appreciable  inclination  to  the 
axis  of  zero  volume.  At  the  right,  the  iso- 
thermal shows  a  decided  break  and  slopes 
away  as  the  volume  becomes  larger  than 
that  of  the  saturated  vapor.  The  isothermal 
for  21°.  5  shows  similar  characteristics,  but 
the  passages  from  one  condition  to  another  are  more  gradual. 
The  dotted  curve  is  drawn  through  the  points  of  saturation  and 
liquefaction,  and  its  crest  corresponds  to  the  critical  temperature. 

*  Phil.  Trans.,  1869,  part  ii,  p.  575,  and  18.76,  part  ii,  p.  421. 


WO-, 
'Jo 
90 
85- 

80- 
75- 
70 
65 
CO 
65  H 
50 


FIG.  aga. 


DENSITY   AT    HIGH    PRESSURE  71 

The  isothermal  for  31. °i  is  clearly  above  the  critical  tempera- 
ture and  does  not  indicate  a  liquefaction. 

The  several  states  of  a  fluid  may  be  enumerated  as 

1.  Liquid. 

2.  Saturated  vapor,  including  mixtures  of  liquid  and  vapor. 

3.  Superheated  vapor  characterized  by  a  larger  volume  than 

saturated  vapor  for  a  given  temperature  and  pressure. 

4.  Gas;  near  the  critical  temperature  the  deviations  from 

Boyle's  law  are  very  large,  at  higher  temperature  the 
deviations  diminish  and  become  unimportant. 
Critical    Temperatures.  —  The    following    table    of    critical 
temperatures  and  of  boiling-points  at  atmospheric   pressure  is 
taken  in  part  from  Preston's  "  Theory  of  Heat,"  1904. 


Boiling-Point. 

Critical  Temperature. 

Hydrogen     

-    -    •       -252.°7 

C.   -234.05C. 

Nitrogen  

.  .  .      -194.4 

—  146 

Oxygen     

.  .  .      -182.2 

-118.8 

Air    

-191.4 

—  140 

Carbon  monoxide    .    .    .    . 

.  .  .      —190 

—  139.5 

Carbon  dioxide    

.  .  .    -78.3 

+  31-35 

Sulphur  dioxide  

.    .    .        —  10 

+  157.0 

Ether    

•    -    -           34-5 

175 

Alcohol     

78.4 

248 

Carbon  bisulphide      .    .    . 

43-3 

254 

Water       

.      .      .                   100 

362 

Density  at  High  Pressure.  —  If  the  usual  methods  (given  on 
page  58)  for  the  solution  of  problems  involving  the  properties 
of  gases,  are  applied  with  very  high  pressure,  errors  amounting 
to  two  or  three  per  cent  are  liable  to  be  incurred,  owing  to  the 
deviation  from  Boyle's  law.  In  some  cases,  this  error  may  be 
ignored  in  engineering  practice;  in  some  cases  the  error  may  be 
included  in  a  practical  factor,  as  will  be  indicated  in  the  design  of 
air  compressors;  and  in  other  cases  allowances  must  be  made 
from  the  experimental  information  furnished  by  Armagat,  and 
which  may  be  found  in  Landolt  and  Bernstein's  Tables. 


72  PERFECT   GASES 

Rontgen's  Experiments.  —  Direct  experiments  to  determine 
K  may  be  made  as  follows.  Suppose  that  a  vessel  is  filled  with 
air  at  a  pressure  plt  while  the  pressure  of  the  atmosphere  is  pa. 
Let  a  communication  be  opened  with  the  atmosphere  sufficient 
to  suddenly  equalize  the  pressure;  then  let  it  be  closed,  and  let 
the  pressure  p2  be  observed  after  the  air  has  again  attained  the 
temperature  of  the  atmosphere.  If  the  first  operation  is  suffi- 
ciently rapid  it  may  be  assumed  to  be  adiabatic,  and  we  may 
use  equation  (77),  from  which 

*  =  !og  *  -  !og  *• 

log  va  —  log  vl 


The  second  operation  is  at  constant  volume;  consequently 
the  specific  volume  is  the  same  at  the  final  state  as  after  the 
adiabatic  expansion  of  the  first  operation.  But  the  initial  and 
final  temperatures  are  the  same;  consequently 


.'.  log  va  —  log  vi  =  log  p,  —  log  p2, 
which  substituted  in  equation  (91)  gives 

log  fr  -  log  p. 


The  same  experiment  may  be  made  by  rarefying  the  air  in 
the  vessel,  in  which  case  the  sign  of  the  second  term  changes. 

Rontgen*  employed  this  method,  using  a  vessel  containing 
70  litres,  and  measuring  the  pressure  with  a  gauge  made  on 
the  same  principle  as  the  aneroid  barometer.  Instead  of  assum- 
ing the  pressure  pa  at  the  instant  of  closing  the  stop-cock  to  be 
that  of  the  atmosphere,  he  measured  it  with  the  same  instrument. 
A  mean  of  ten  experiments  on  air  gave 

tc  =  1.4053. 

*  Poggendorft's  Annalen,  vol.  cxlviii,  p.  580. 


EXAMPLES  73 

EXAMPLES. 

1.  Find  the  weight  of  4  cubic  metres  of  hydrogen  at  30°  C., 
and  under  the  pressure  of  800  mm.  of  mercury.     Ans.  0.341  kg. 

2.  Find  the  volume  of  3  pounds  of  nitrogen  at  a  pressure  of 
45  pounds  to  the  square  inch  by  the  gauge  and  at  80°  F.     Ans. 

10.33- 

3.  Find  the  temperature  at  which  one  kilogram  of  air  will 

occupy  one  cubic  metre  when  at  a  pressure  of  20,000  kilograms 
per  square  metre.     Ans.  410°  C. 

4.  Oxygen  and  hydrogen  are  to  be  stored  in  tanks  10  inches 
in  diameter  and  35  inches  long.     At  a  maximum  temperature 
of   no°F.,  the  pressure  must  not   exceed   250   pounds  gauge. 
What  weight  of  oxygen  can  be  stored  in  one  tank?     What  of 
hydrogen?     Ans.  Oxygen  2.21  pounds.     Hydrogen  0.138  pound. 

5.  A  balloon  of  12,000  cubic  feet  capacity,  weighing  with  car, 
occupant,   etc.,   665   pounds,   is    inflated   with  9500  cubic  feet 
hydrogen   at   60°  F.,    the   barometer   reading   30  inches.     Find 
the  weight  of  the  hydrogen  and  the  pull  on  the  anchor  rope; 
find  also  the  amount  that  the  balloon  must  be  lightened  to  reach 
a  height  where  the  barometer  reads  20  inches,  and  the  tempera- 
ture   is    10°    below    zero    Fahrenheit.     Ans.    Weight    hydrogen 
50.4  pounds;  pull  on  rope   12   pounds;  balloon   lightened   7.5 
pounds. 

6.  A  gas-receiver  holds  14  ounces  of  nitrogen  at  20°  C.,  and 
under  a  pressure  of  29.6  inches  of  mercury.     How  many  will  it 
hold  at  32°  F.,  and  a  I  the  normal  pressure  of  760  mm.  ?     Ans. 
15.18  ounces. 

7.  A  gas-receiver  having  the  volume  of  3  cubic  feet  contains 
half  a  pound  of  oxygen  at  70°  F.     What  is  the  pressure  ?     Ans. 
29.6  pounds  per  square  inch. 

8.  Two  cubic  feet  of    air  expand  at  50°  F.  from  a  pressure 
of  80  pounds  to  a  pressure  of  60  pounds  by  the  gauge.     What 
is  the  external  work?     Ans.  6464  foot-pounds. 

9.  What  would   have   been   the   external  work  had   the  air 
expanded  adiabatically  ?    Ans.  4450  foot-pounds. 


74  PERFECT    GASES 

10.  Find  the  external  work  of  2  pounds  of  air  which  expand 
adiabatically  until   the  volume  is  doubled,  the   initial   pressure 
being  100  pounds  absolute  and  the  initial  temperature  100°  F. 
Ans.  36,100  foot-pounds. 

11.  Find   the   external  work  of   one   kilogram   of  hydrogen, 
which,  starting  with  the  pressure  of  4  atmospheres  and  with  the 
temperature  of  500°  C.,  expands  adiabatically  till  the  tempera- 
ture becomes  30°  C.     Ans.  489,000  m.-kg. 

12.  Find    the    exponent    for    an    exponential    curve    passing 
through    the    points  p  =  30,   v  =  1.9,   and  pl  =  15,   tvl  =  9.6. 
Ans.  0.4279. 

13.  Find  the  exponent  for  a  curve  to  pass  through  the  points 
p  =  40,  v  =  2,  and  pi  =  12,  vl  =  6.     Ans.  1.0959. 

14.  In  examples  12  and  13  let  p  be  the  pressure  in  pounds  on 
the  square  inch  and  v  the  volume  in  cubic  feet.     Find  the  external 
work  of  expansion  in  each  case.     Ans.  21,900  and  12,010  foot- 
pounds. 

15.  Find  the  intrinsic  energy  of  one  pound  of  nitrogen  under 
the  standard  pressure  of  one  atmosphere  and  at  freezing-point 
of  water.     Ans.  66,500  foot-pounds. 

1 6.  A  cubic  foot  of  air  at  492.7°  F.  exerts  14.7  pounds  gauge 
pressure  per  square  inch.     How  much  do  its  internal  energy  and 
its  entropy  exceed  those  of  the  same  air  under  standard  condi- 
tions?    Ans.  5052  foot-pounds;  .00912  units  of  entropy. 

17.  Find  the  increase  in  entropy  of  2  pounds  of  a  perfect  gas 
during  isothermal  expansion  at  100°  F.  from  an  initial  pressure 
of  84.3  pounds  gauge  and  a  volume  of  20  cubic  feet  to  a  final 
volume  of  40  cubic  feet.     Ans.  0.453. 

1 8.  A  kilogram  of  oxygen  at  the  pressure  of  6  atmospheres 
and  at  100°  C.  expands  isothermally  till  it  doubles  its  volume. 
Find  the  change  of  entropy.     Ans.  0.0434. 

19.  Twenty  pounds   of  air  are  heated  at  a  constant  pressure 
of  200  pounds  absolute  per  square  inch  until  the  volume  increases 
from  20  cubic  feet  to  40  cubic  feet.     Find  the  initial  and  final 
temperatures,  the  change  in  internal  energy  and  the  increase  in 
entropy.     How    much    heat    is    added?     Ans.    80°    and    620°; 


EXAMPLES 


75 


increase  of  intrinsic  energy  1,420,000  foot-pounds;  increase  in 
entropy  3.29;  heat  2570  B.T.U. 

20.  Suppose  a  hot-air  engine,  in  which  the  maximum  pressure 
is  100  pounds  absolute,  and  the  maximum  temperature  is  600°  F., 
to  work  on  a  Carnot  cycle.  Let  the  initial  volume  be  2  cubic 
feet,  let  the  volume  after  isothermal  expansion  be  5  cubic  feet, 
and  the  volume  after  adiabatic  expansion  be  8  cubic  feet.  Find 
the  horse-power  if  the  engine  is  double-acting  and  makes  30 
revolutions  per  minute.  Ans.  8.3  horse-power. 


CHAPTER    VI. 

SATURATED  VAPOR. 

FOR  engineering  purposes  steam  is  generated  in  a  boiler  which 
is  partially  filled  with  water  and  arranged  to  receive  heat  from 
the  fire  in  the  furnace.  The  ebullition  is  usually  energetic,  and 
more  or  less  water  is  mingled  with  the  steam;  but  if  there  is  a 
fair  allowance  of  steam  space  over  the  water,  and  if  proper 
arrangements  are  provided  for  withdrawing  the  steam,  it  will 
be  found  when  tested  to  contain  a  small  amount  of  water,  usu- 
ally between  half  a  per  cent  and  a  per  cent  and  a  half.  Steam 
which  contains  a  considerable  percentage  of  water  is  passed 
through  a  separator  which  removes  almost  all  the  water.  Such 
steam  is  considered  to  be  approximately  dry. 

If  the  steam  is  quite  free  from  water  it  is  said  to  be  dry  and 
saturated;  steam  from  a  boiler  with  a  large  steam  space  and 
which  is  making  steam  very  slowly  is  nearly  if  not  quite  dry. 

Steam  which  is  withdrawn  from  the  boijer  may  be  heated  to  a 
higher  temperature  than  that  found  in  the  boiler,  and  is  then  said 
to  be  superheated. 

The  physical  properties  of  both  saturated  and  superheated 
steam  have  now  been  determined  by  methods  susceptible  of 
certainty  and  precision  so  that  computations  based  on  them 
show  satisfactory  concordance.  The  results  of  these  investiga- 
tions will  be  quoted  directly  from  the  original  authorities, 
together  with  their  estimate  of  the  degree  of  precision  to  be 
attributed  to  their  results.  This  matter  should  be  read  with 
care,  so  that  each  one  may  determine  for  himself  the  confidence 
he  can  have  in  the  tables  based  upon  it  and  the  accuracy  of 
computation  made  by  their  aid. 

Saturated  Steam.  —  The  essential  properties  of  saturated  steam 
are  heat  of  the  liquid,  heat  of  vaporization,  specific  pressure  and 
specific  volume;  other  properties  dependent  on  these  are  heat 

76 


UNIT    OF    HEAT  77 

equivalent  of  external  work,  heat  equivalent  of  internal  work, 
entropy  of  the  liquid  and  entropy  of  vaporization.  All  these 
properties  depend  on  the  temperature  only,  and  may  conven- 
iently be  determined  and  tabulated  for  use  in  solving  engineering 
problems.  The  author's  Tables  of  the  Properties  of  Steam,  etc., 
have  been  prepared  for  this  purpose. 

Standard  Temperature.  —  It  is  customary  to  refer  all  calcula- 
tions for  gases  to  the  standard  conditions  of  the  pressure  of  the 
atmosphere  (760  mm.  of  mercury)  and  to  the  freezing-point  of 
water.  Formerly  the  freezing-point  was  taken  as  the  standard 
temperature  for  water  and  steam  as  even  now  it  is  the  initial  point 
for  tables  of  the  properties  of  saturated  vapors.  But  the  investi- 
gation of  the  mechanical  equivalent  of  heat  by  Rowland  resulted 
in  a  determination  of  the  specific  heat  of  water  with  much  greater 
delicacy  than  is  possible  by  the  method  of  earlier  experimenters, 
and  showed  that  the  freezing-point  is  not  well  adapted  for  the 
standard  temperature  for  water.  It  is  the  habit  of  many  physi- 
cists to  take  15°  C.  as  the  standard  temperature,  and  this  cor- 
responds substantially  with  62°  F.,  at  which  the  English  units  of 
measure  are  standard. 

Unit  of  Heat.  —  The  unit  for  the  measurement  of  heat  is  the 
amount  of  heat  required  to  raise  one  unit  of  weight  of  water  one 
degree  from  the  standard  temperature. 

The  calorie  is  the  amount  of  heat  required  to  raise  the  temper- 
ature of  one  kilogram  of  water  from  15°  to  16°  C. 

The  British  Thermal  Unit  is  the  amount  of  heat  required  to 
raise  the  temperature  of  one  pound  of  water  from  62°  to  63°  F. 

These  two  definitions  lead  to  a  discrepancy  of  0.03  of  one  per 
cent,  which  is  insignificant  for  engineering  purposes;  in  the 
author's  tables  the  B.T.U.  is  taken  as  the  standard,  and  the  dis- 
crepancy noted  is  ignored* 

Some  physicists  prefer  to  use  for  the  unit  of  heat,  one  hun- 
dredth part  of  the  heat  required  to  raise  a  kilogram  of  water  from 
freezing-point  to  boiling-point.  Such  a  mean  calorie  is  greater 
than  those  defined  above,  by  0.2  of  one  per  cent.  It  requires 
also  that  a  different  value  shall  be  assigned  to  the  mechanical 
equivalent  of  heat  than  that  given  in  the  following  section. 


78  SATURATED   VAPOR 

Mechanical  Equivalent  of  Heat. — If  mechanical  energy  or  work 
is  transformed  into  heat  and  applied  to  heating  water,  it  will  be 
found  that  778  foot-pounds  of  work  will  be  required  to  heat  one 
pound  of  water  from  62°  to  63°  F.;  in  other  words,  one  B.T.U. 
is  equivalent  to  that  number  of  foot-pounds.  This  is  known  as 
the  mechanical  equivalent  of  heat.  The  most  authoritative 
determination  of  this  important  constant  appears  to  be  that  by 
Rowland,*  who  gives  the  value  quoted,  namely, 

778  foot-pounds. 
This  is  equivalent  to 

427  metre  kilograms 

in  the  metric  system.  Since  his  experiments  were  made,  this 
important  physical  constant  has  been  investigated  by  several 
experimenters,  and  also  a  recomputation  of  his  results  has  been 
made  after  a  recomparison  of  his  thermometers.  The  conclusion 
appears  to  be  that  his  results  may  be  a  little  small,  but  the  differ- 
ences are  not  important,  and  it  is  not  certain  that  the  conclusion 
is  valid.  There  seems,  therefore, no  sufficient  reason  for  changing 
the  accepted  values  given  above. 

Specific  Heat  is  the  number  of  thermal  units  required  to  raise 
a  unit  of  weight  of  a  given  substance  one  degree  of  temperature. 
The  specific  heat  of  water  at  standard  temperature  is  unity,  and 
any  specific  heat  is  essentially  a  ratio. 

Specific  Heat  of  Water.  —  The  most  reliable  determination  of 
the  specific  heat  of  water  is  that  by  Dr.  Barnes,f  who  used  an 
electrical  method  devised  by  Professor  Callendar  and  himself, 
and  who  extended  the  method  to  and  below  freezing-point  by 
carefully  cooling  water  without  the  formation  of  ice  to  —  5°  C. 
This  method  gives  relative  results  with  great  refinement,  and 
gives  also  a  good  confirmation  of  Rowland's  determination  of  the 
mechanical  equivalent  of  heat.  Dr.  Barnes  reports  values  of  the 
specific  heat  of  water  up  to  95°  C. 

For  temperatures  above  boiling-point  values  of  the  specific  heat 
of  water  have  been  determined  by  the  author  from  Regnault's  J 

*  Proc.  Am.  Acad.,  vol.  xv  (N.  S.  vii),  1879. 

t  Physical  Review,  vol.  xv,  p.  71,  1902. 

i  Memoir es  de  I'  Institut  de  France,  etc.,  tome  xxvi. 


SPECIFIC    HEAT   OF   WATER 


79 


experiments  on  the  heat  of  the  liquid,  allowing  for  the  correct 
specific  heat  of  the  water  in  his  calorimeter  from  Barnes's  work. 
The  probable  error  of  the  heats  of  the  liquid  thus  obtained, 
appears  to  be  one-fourth  of  a  per  cent.  But  the  heat  of  the 
liquid  for  temperatures  above  boiling-point  is  habitually  asso- 
ciated with  the  heat  of  vaporization,  and  the  above  error  is  less 
than  one-tenth  per  cent  of  their  sum. 

In  the  following  table  Barnes's  results  are  quoted  directly  from 
o°  to  55°  C.;  from  55  to  95  degrees  his  results  have  been  slightly 
increased  to  join  with  results  determined  by  recomputing 
Regnault's  experiments  on  the  heat  of  the  liquid  for  water  by 
allowing  for  the  true  specific  heat  at  low  temperature  from  Dr. 
Barnes's  experiments.  The  maximum  effect  of  modifying  Dr. 
Barnes's  results  is  to  increase  the  heat  of  the  liquid  at  95  degrees 
by  one-tenth  of  one  per  cent. 


Temperature. 

Temperature. 

Temperature. 

Specific 

Specific 

Specific 

Heat. 

Heat. 

Heat. 

C. 

F. 

C. 

F. 

C. 

F. 

0 

32 

1.0094 

45 

113 

0.99760 

90 

194 

1.00705 

5 

41 

1.00530 

50 

122 

0.99800 

95 

103 

1.00855 

10 

50 

1.00230 

55 

131 

0.99850 

100 

212 

1.01010 

15 

59 

1.00030 

60 

140 

0.99940 

120 

248 

1.01620 

20 

68 

0.99895 

65 

149 

1.00040 

140 

284 

1.02230 

25 

77 

0.99806 

70 

158 

1.00150 

160 

320 

1.02850 

30 

86 

0.99759 

75 

167 

1.00275 

180 

356 

1.03475 

35 

95 

0.99735 

80 

176 

1.00415 

200 

392 

1.04100 

40 

104 

0.99735 

85 

188 

1.00557 

220 

428 

1.04760 

The  specific  heats  of  water  at  high  temperatures  have  been 
determined  by  Dieterici  *  using  a  method  which  does  not  appear 
to  have  the  certainty  of  Barnes's  method.  His  results  appear  to 
be  systematically  larger  than  Barnes's  results,  the  discrepancy  at 
95°  C.  being  four-tenths  of  a  per  cent.  Should  his  specific  heats 
be  used  to  determine  the  heat  of  the  liquid  at  200°  C.,  the  results 
would  appear  to  be  four-tenths  of  a  per  cent  larger  than  the  values 
of  the  heat  of  the  liquid  at  200°  C.,  in  the  author's  tables.  Even 
so  if  this  be  compared  with  the  sum  of  the  heat  of  the  liquid  and 

*  Annalen  der  Physik,  vol.  16,  part  4,  p.  593,  1905. 


8o  SATURATED   VAPOR 

the  heat  of  vaporization,  the  discrepancy  becomes  about  one-tenth 
of  a  per  cent. 

Heat  of  the  Liquid.  —  The  heat  required  to  raise  one  unit  of 
weight  of  any  liquid  from  freezing-point  to  a  given  temperature 
is  called  the  heat  of  the  liquid  at  that  temperature. 

If  the  specific  heat  of  water  were  constant  the  heat  of  the  liquid 
would  be  found  by  multiplying  the  increase  of  temperature  by 
the  specific  heat.  An  approximate  result  can  be  obtained  by 
using  the  mean  specific  heat.  For  example,  the  mean  specific 
heat  from  o°  to  25°  C.  may  be  taken  to  be  -§-(J  X  1.0094  +  1.00530 
-I-  1.00230  +  1.00030  +  0.99895  +  J  X  0.99806)  =  1.00212, 
and  25  X  i. 00212  =  25.05, 

which  in  this  case  corresponds  exactly  with  the  value  in  the 
author's  tables. 

The  integral  calculus  gives  for  a  varying  specific  heat  the 
expression 

q  =  Ccdt 

for  the  heat  of  the  liquid.  An  equivalent  of  the  operation  repre- 
sented by  this  equation  is  to  draw  a  curve  with  temperatures  and 
specific  heats  as  coordinates  and  to  measure  the  area  under  that 
curve.  The  fact  that  the  specific  heat  does  not  vary  much  from 
unity  suggests  the  following  method : 

Let  c  =  i  +  k 

where  k  is  the  difference  between  the  specific  heat  and  unity;  it 
may  be  positive  or  negative  as  the  case  may  be.  Then 


-  t  +  Ckdt, 


which  leads  to  a  convenient  graphical  method  since  k  is  always 
small,  and  the  diagram  may  be  drawn  with  a  large  scale  for 
ordinates,  and  accurate  results  can  be  obtained.  The  values  for 
the  heat  of  the  liquid  in  the  tables  were  obtained  in  this  way. 

The  following  table  gives  equations  for  heats  of  the  liquid  for 
various  substances  as  determined  by  Regnault :  * 

*  Memoir es  de  I'Inslitut  de  France,  etc.,  tome  xxvi. 


TOTAL   HEAT  8l 

HEAT  or  THE  LIQUID. 

Alcohol q  =  0.54754^  +  o.ooii2i8/2  4-  0.000002206** 

Ether q  =  0.52901  /  +  0.0002959^ 

Chloroform q  =  0.23235 1  +  0.0000507^ 

C arbon  bisulphide.,  .q  =  0.23523^  +  o.ooooSi^/2 
Carbon  tetrachloride  q  =  o.igjgSt  +  0.0000906^ 
Aceton q  =  0.50643  /  +  0.0003965 /2 

Heat  of  Vaporization.  —  If  a  unit  of  weight  of  a  liquid  be  at 
a  certain  temperature  and  subject  to  the  corresponding  pressure, 
then  the  amount  of  heat  required  to  entirely  vaporize  it  into  dry 
saturated  vapor  at  that  temperature  and  against  that  pressure, 
is  called  the  heat  of  vaporization.  Henning*  gives  the  following 
formula  for  the  heat  of  vaporization  of  a  kilogram  of  water  in 
calories, 

r  =  94.210  (365  -  0  »•'"" (93) 

He  gives  as  the  probable  error  of  this  equation  one-tenth  of  one 
per  cent.  Other  experiments  by  Dieterici,f  Griffiths,!  and  A.  C. 
Smith  §  are  represented  by  this  equation  with  a  like  degree  of 
precision. 

The  heat  of  vaporization  of  one  pound  of  water  in  B.T.U. 
is  given  by  the  following  equation,  obtained  by  transforming 

equation  (93). 

r  =  141.124  (689  -  /)  °'31249 (94) 

Both  of  the  above  equations  are  applicable  from  freezing  to 
boiling-point;  equation  (93)  fromo0  to  100°  C.,  and  equation  (94) 
from  32°  to  2i2°F. 

Total  Heat.  —  The  amount  of  heat  required  to  raise  a  unit  of 
weight  of  a  liquid  from  freezing-point  to  a  given  temperature  and 
to  vaporize  it  into  dry  saturated  vapor  against  the  corresponding 
pressure  is  called  the  total  heat. 

The  quantity  is  clearly  equal  to  the  sum  of  the  heat  of  the 
liquid  and  the  heat  of  vaporization;  if  the  first  is  represented  by 

*  Annalen  der  Physik,  vol.  21,  part  4,  p.  849,  1906. 
t  Annalen  der  Physik,  vol.  16,  part  4,  p.  912,  1905. 
%  Phil.  Trans.  186,  p.  261,  1895;  P-  593> 
§  Physical  Review,  vol.  xxv,  1907. 


82  SATURATED    VAPOR 

q  and  the  latter  by  r,  then  H,  the  total  heat,  is  given  by  the 

following  equation, 

H  =  r  +  q (95) 

Conversely,  if  H  and  q  are  known,  the  preceding  equation  will 
give  r. 

From  an  investigation  of  certain  experiments  on  the  super- 
heating of  steam  by  throttling,  Dr.  Harvey  N.  Davis*  gives  for 
the  total  heat  of  steam  in  B.T.U.  per  pound, 

H    =  H212   +  0.3745   (/   -   212)    -  0.000550  (/   -   2I2)2,       (96) 

in  which  H212  is  the  total  heat  at  boiling-point.  Equation  (94) 
gives  for  the  heat  of  vaporization  at  boiling-point  969.7,  and  the 
method  on  page  80,  for  finding  the  heat  of  the  liquid,  gives  180.3 
at  that  temperature,  consequently  the  above  equation  may  be 
written,  for  English  units, 

H  ==  1150  +  0.3745  (/  -  212)  -  0.000550  (/  -  2i2)2.  (97) 

For  French  units  the  equation  takes  the  form 

H  =  638.9  +  0.3745  (/  —  100)  —  0.00099  (^  ~  ioo)2-    (98) 

Davis  gives  one-tenth  of  one  per  cent  for  the  probable  error 
of  this  equation. 

For  other  liquids  the  heats  of  vaporization  are  given  by  Regnault. 

Ether H  =  94  +  0.45  /  —  0.00055556^ 

.    Chloroform H  =  67  +  0.1375  / 

Carbon  bisulphide H  =  90  +  0.14601^  —  0.00041 23 /' 

Carbon  tetrachloride. . .  H  =  52  +  0.14625 1  -  0.000172^ 

Aceton H  =  140.5  +  0.36644^  —  0.0005 16/2 

Specific  Pressure.  —  It  is  customary  to  develop  theoretical 
thermodynamic  equations  with  the  specific  pressure  expressed  in 
pounds  per  square  foot,  for  English  units.  Engineers  habitually 
express  pressures  in  pounds  per  square  inch. 

For  French  units,  specific  pressures  are  expressed  in  kilograms 
per  square  meter.  Engineers  use  kilograms  per  square  centi- 
meter, and  on  the  other  hand  physicists  commonly  express 
pressure  in  millimeters  of  mercury. 

One  cubic  decimeter  (or  one  liter)  of  mercury  weighs  13.5959 
kilograms,  and  a  cubic  decimeter  is  one-thousandth  of  a  cubic 

*  Trans.  Ant.  Soc.  Mech.  Eng.t  1908. 


PRESSURE   OF   SATURATED    STEAM  83 

meter,  consequently  the  pressure  of  a  column  of  mercury  one  milli- 
meter high,  on  a  base  one  meter  square,  is  13.5959  kilograms. 

The  normal  pressure  of  the  atmosphere  is  taken  to  be  760  mm. 
of  mercury  (at  o°  C.),  which  is  equivalent  to  10,333  kilograms 
per  square  meter.  The  normal  pressure  of  the  atmosphere  is, 
therefore,  1.0333  kilograms  per  square  centimeter.  It  was  for- 
merly the  custom  to  graduate  pressure  gauges  in  atmospheres,  for 
use  in  countries  using  the  metric  system.  There  is  a  tendency 
to  confusion  of  units  that  are  roughly  approximate,  and  in  some 
cases  it  is  necessary  to  determine  whether  a  pressure  is  intended 
to  be  in  atmospheres  or  in  kilograms  per  square  centimeter. 

Taking  the  meter  to  be  equivalent  to  39.37  inches,  and  the 
kilogram  to  weigh  2.20462  pounds,  then  one  millimeter  of  mercury 
will  be  equivalent  to 

13.5959  x  2.20462^  =  _oi933g 

39-372 

of  a  pound  per  square  inch.  The  normal  pressure  of  the  atmos- 
phere is  760  times  this,  or  14.696  pounds  per  square  inch.  The 
corresponding  specific  pressure  is  2116  pounds  per  square  foot. 

Pressure  of  Saturated  Steam.  —  Recent  determinations  of  the 
pressure  of  saturated  steam  have  been  made  by  Holborn  and 
Henning*  with  all  the  resources  of  modern  physical  methods 
including  the  platinum  thermometer.  Their  results  reduced  to 
the  thermometric  scale  are  set  down  in  Table  III  of  the  author's 
tables,  exactly  as  given  in  their  original  report.  Their  own  tests 
covered  the  range  of  temperature  from  50°  C.  to  200°  C.,  but  they 
extend  their  results  to  205°  C.  The  results  which  they  give  from 
freezing-point  to  50°  C.  were  deduced  by  them  from  experiments 
of  Thiesen  and  Scheel.  In  Table  III  the  pressures  from  205°  to 
220°  C.  are  extrapolated  by  the  author  by  aid  of  a  curve  of 
corrections  for  Regnault's  equation  for  the  range  100°  to  220°  C. 

Holborn  and  Henning  attribute  to  their  own  experiments  a 
precision  of  T£<J  of  a  degree  Centigrade;  this  is  far  beyond 
technical  requirements  for  direct  application,  but  is  needed  in 
the  computation  of  specific  volumes,  as  will  appear  later.  Thiesen 

*  Annalen  der  Physik,  vol.  26,  part  4,  p.  833, 1908. 


84 


SATURATED   VAPOR 


and  Scheel's  experiments  had  a  less  degree  of  precision;  and  the 
extrapolation  from  205°  to  220°  C.  is  open  to  some  doubt. 

Pressures  of  Other  Vapors.  —  Regnault  determined  the  pres- 
sures of  various  vapors  and  deduced  for  all  of  them  equations 

having  the  form 

log  p  =  a  +  ban  +  cfin.  (99) 

The  following  table  gives  the  special  forms  of  the  equation 
and  the  constants  for  several  vapors: 


log  a. 

a. 

b. 

c. 

Alcohol             

a  —  ban  -f  cy?n 
a  +  ban  —  cftn 
a  —  ban  —  cfin 
a  -  ban  -  cpn 
CL  —  ban  —  cBn 

5.4562028 
5.0286298 
5.2253893 
5.4011662 
12.0962331 

4.9809960 
0.0002284 
2.9531281 
3.4405663 
9.1375180 

0.0485397 
3.1906390 
0.0668673 
0.2857386 
1.9674890 

Ether            

Chloroform  
Carbon  bisulphide  
Carbon  tetrachloride.  .  . 

log  a. 

,0,,. 

n. 

Limits. 

Alcohol        ... 

9.99708557-10 
0.0145775  -10 
9.9974144  -10 
9.9977628  -10 
9.9997120  -10 

9.9409485  -10 
9.996877  -10 
9.9868176  -10 
9.9911997  -10 
9.9949780-10 

t  +  20 
t+  20 
t-  20 
t+  20 
t+  20 

-  20°,  +  150°  C. 
-  20°,  +  120°  C. 
+  20°,  +  164°  C. 
-  20°,  +  140°  C. 
-  20°,  +  188°  C. 

Ether            

Chloroform  
Carbon  bisulphide  .  .  . 
Carbon  tetrachloride. 

Zeuner*  gives  the  following  equation  for  aceton  based  on 
Regnault's  work: 

log      p  =  a  —  ban  +  c/?n; 

a  =  5-3°854i9; 

log  ban  =  +  0.5312766  —  0.0026148 /; 
log  cj3n  =  —  0.9645222  —  0.0215592  /. 

Specific  Volume  of  Liquids.  —  The  coefficient  of  expansion  of 
most  liquids  is  large  as  compared  with  that  of  solids,  but  it  is 
small  as  compared  with  that  of  gases  or  vapors.  Again,  the 
specific  volume  of  a  vapor  is  large  compared  with  that  of  the 
liquid  from  which  it  is  formed.  -  Consequently  the  error  of 
neglecting  the  increase  of  volume  of  a  liquid  with  the  rise  of 
temperature  is  small  in  equations  relating  to  the  thermodynamics 
of  a  saturated  vapor,  or  of  a  mixture  of  a  liquid  and  its  vapor 
when  a  considerable  part  by  weight  of  the  mixture  is  vapor.  It 

*  Mechanische  Warmetheorie. 


SPECIFIC    VOLUME    OF   LIQUIDS  85 

is,  therefore,  customary  to  consider  the  specific  volume  of  a  liquid 
to  be  constant. 

The  following  table  gives  the  specific  gravities  and  specific 
volumes  of  liquids. 

SPECIFIC  GRAVITIES   AND  SPECIFIC   VOLUMES  OF   LIQUIDS. 


Specific 
Gravity 
compared 
with  Water 
at  4°  C. 

Specific  Volume. 

Cubic  Metres. 

Cubic  Feet. 

Alcohol                              

0.  80625 
0.736 
1.527 
1.2922 
1.6320 
0.81 
1.4336 
0.6364 
1 

0.001240 
0.001350 
0.000655 
0.000774 
0.00613 
0.00123 
0.0006981 
0.001571 
0.001 

0.0112 
0.0252 
0.01602 

Ether                         

Chloroform.    .  .         

Carbon  bisulphide 

Carbon  tetrachloride 

Aceton 

Sulphur  dioxide                                      .  . 

Ammonia                                      

Water      

Volumes  of  Liquids.  —  The  volumes  of  liquids  at  high  tem- 
peratures, compared  with  the  volume  at  freezing-point,  are  repre- 
sented by  the  following  equations  given  by  Him :  *  — 


Water  100°  C.  to  200°  C.  (vol. 
at  4°C.  =  unity) v-- 


Alcohol  30°  C.  to  160°C.  (vol. 
at  0°C.  =  unity) v- 


Ether  30°  C.  to  130°  C.  (vol.  at 
0°C.  =  unity) v- 


Carbon  bisulphide  30°  to  160° 
C.  (vol.  at  0°C.  =  unity).  .  .v- 


Carbon  tetrahcloride  30°  to  160° 
C.  (vol.  at  0°C.  =  unity) v-- 


1  +  0.00010867875* 
+  0.0000030073653*2 
+  0.0000000028730422*3 
-  0  .  0000000000066457031*4 

1  +  0.00073892265* 
+  0.00001055235*2 
-0.000000092480842*3 
+  0  .  00000000040413567*4 


0013489059* 
+  0.0000065537*2 
-0.000000034490756*3 
+  0  .  00000000033772062*4 

1  +  0.0011680559* 
+  0.0000016489598*2 
-0.00000000081119062*' 
+  0  .  000000000060946589*4 

1  +  0.0010671883* 
+  0.0000035651378*2 
-0.  00000001  4949281*3 
+  0  .  000000000085182318*- 


Logs. 

6.0361445-10 
4.4781862-10 
1.4583419-10 
8.8225409-20 

6.8685991-10 
3.0233492-10 
2.9660517-10 
0.6065278-10 

7.1299817-10 
4.8164866-10 
2.5377028-10 
0.5285571-10 

7.0674636-10 
4.2172103-10 
0.9091229-10 
8.7849494-20 

7.0282409-10 
4.5520763-10 
2.1746202-10 
9.9303494-20 


*  Annales  de  Chimie  et  de  Physique,  1867, 


86  SATURATED   VAPOR 

Internal  and  External  Latent  Heat.  —  The  heat  of  vaporization 
overcomes  external  pressure,  and  changes  the  state  from  liquid 
to  vapor  at  constant  temperature  and  pressure.  Let  the  specific 
volume  of  the  saturated  vapor  be  s,  and  that  of  the  liquid  be  a, 
then  the  change  of  volume  is  5  —  a  =  u,  on  passing  from  the 
liquid  to  the  vaporous  state.  The  external  work  is 
p  (s  -  a]  =  pu, 

and  the  corresponding  amount  of  heat,  or  the  external  latent 
heat,  is 

Ap  (s  —  o)=  ApUj 

A  being  the  reciprocal  of  the  mechanical  equivalent  of  heat. 

That  part  of  the  heat  of  vaporization  which  is  not  used  in  doing 
external  work  is  considered  to  be  used  in  changing  the  state  from 
liquid  to  vapor.  This  work  required  to  change  the  molecular 
arrangement  is  called  disgregation  work.  The  heat  required  to 
do  the  disgregation  work  is  represented  by 

p  =  r  —  Apu.  (100) 

Quality  or  Dryness  Factor.  —  All  the  properties  of  saturated 
steam,  such  as  pressure,  volume,  and  heat  of  vaporization,  depend 
on  the  temperature  only,  and  are  determinable  either  by  direct 
experiment  or  by  computation,  and  are  commonly  taken  from 
tables  like  the  Tables  of  the  Properties  of  Steam,  etc. 

Many  of  the  problems  met  in  engineering  deal  with  mixtures 
of  liquid  and  vapor,  such  as  water  and  steam.  In  such  problems 
it  is  convenient  to  represent  the  proportions  of  water  and  steam 
by  a  variable  known  as  the  quality  or  the  dryness  factor;  this 
factor,  x,  is  defined  as  that  portion  of  each  pound  of  the  mixture 
which  is  steam;  the  remnant,  i  —  x,  is  consequently  water. 

Specific  Volume  of  Wet  Steam.  —  If  a  pound  of  a  homogeneous 
mixture  of  water  and  steam  is  x  part  steam,  then  the  specific 
volume  may  be  represented  by 

V   =   XS   +    (l    —   X)  O   =   XU   -f    (7,  (lOl) 

where  u  is  the  increase  of  volume  due  to  vaporization. 

General  Equation.  —  In  order  to  apply  the  general  thermo- 
dynamic  method  to  a  mixture  of  a  liquid  and  its  vapor,  it  is 


APPLICATION    OF   THE   FIRST    LAW  87 

customary  to  write  a  differential  equation  involving  the  tem- 
perature ty  the  quality  x,  the  specific  heats  of  water  and  steam 
c  and  h,  and  the  heat  of  vaporization  r;  these  last  three  properties 
are  functions  of  the  temperature  only. 

The  principal  result  of  the  application  of  the  general  method 
to  such  an  equation  is  a  formula  for  calculating  the  specific 
volume  s,  as  will  appear  later.  In  addition  to  the  general  method, 
a  special  derivation  of  the  formula  for  s  will  be  given  which  may 
be  preferred  by  some  readers. 

When  a  mixture  of  liquid  and  its  vapor  receives  heat  there  is 
in  general  an  increase  in  the  temperature  of  the  portion  x  of 
vapor  and  in  the  portion  i  —  x  of  liquid,  and  there  is  a  vaporiza- 
tion of  part  of  the  liquid.  Taking  c  for  the  specific  heat  of  the 
liquid  and  h  for  the  specific  heat  of  the  vapor,  while  r  is  the  heat 
of  vaporization,  we  shall  have  for  an  infinitesimal  change, 

dQ  =  hxdt  4-  c  (i  —  x)  dt  +  rdx.  (103) 

Application  of  the  First  Law.  —  The  first  law  of  thermo- 
dynamics is  applied  to  equation  (103)  by  combining  it  with 
equation  (16),  so  that 

dQ  =  A  (dE  +  pdv)  =  hxdt  +  c  (i  -  x)  dt  +  rdx; 

.'.     dE  =  -  [hx  +  c  (i  -  x)]  dt  +  -dx  -  pdv. 
A  A 

Now  v  is  a  function  of  both  t  and  x,  as  is  evident  from  equation 
(101),  in  which  u  is  a  function  of  t;  consequently, 

dv  dv  , 


But  E  being  expressed  in  terms  of  t  and  x  gives 


dx      dx  dt 


88  SATURATED   VAPOR 

Bearing  in  mind  that  all  the  functions  but  x  and  v  are  func 
tions  of  t  only,  the  differentiation  gives  . 


A  dt  dx      Adt       dt  dx         dx  dt 

Equation  (101)  gives 

dv 

Tx  =  M> 
and 


dt  dx      dx  dt  ' 
so  that  the  above  equation  reduces  to 


Application  of  the  Second  Law.  —  The  second  law  of  thermo- 
dynamics makes 


for  a  reversible  process,  so  that  the  general  equation  (103)  may 
be  reduced  to 

dO      hx  +  c  (i  —  x)   ,        r  j 
T=~          T  -  -dt+^dx. 

But 


dxdt       dtdx 
hx  +  c  (i  —x)  __  _£   r_ 

T         ~  dt  r 

T^-r 
h  -  c          ^ 


(»s) 


SPECIAL   METHOD  89 

First    and    Second    Laws    Combined.  —  The    combination    of 
equations  (104)  and  (105)  gives 

r  =AuTd£    ........   (106) 

Special  Method.  —  The  preceding  equation  may  be  obtained 
by  a  special  method  making  use  of  the 

>  diagram  abed  in  Fig.  30,  which  repre- 

sents Carnot's  cycle  for  a  mixture  of  a 

a         T  -  b  liquid    and    its    vapor,    the    change    of 

d  -  T>Sf  -  o  temperature  AT  being  very  small.  Let 
a  represent  the  volume  of  one  pound  of 
water  at  the  temperature  T,  and  b  the 
volume  of  one  pound  of  steam  at  the  same 

FIG.  30. 

temperature  and  pressure.     The  line  ab 

therefore  represents  the  vaporization  of  one  pound  of  water  at 
constant  temperature,  involving  the  application  of  the  heat  of 
vaporization  r,  and  the  increase  of  volume 

u  =  s  —  a, 

where  5  and  a  are  the  specific  volumes  of  steam  and  water.  By 
the  second  law  of  thermodynamics  the  efficiency  of  this  cycle  will 
be 

AT 


T  T 

so  that  the  heat  changed  into  work  will  be 


But  by  the  first  law  of  thermodynamics  this  heat  is  equivalent 
to  the  external  work,  which  in  this  case  is  approximately  equal 
to  the  increase  of  volume  u  multiplied  by  the  change  of  pressure 
A/>;  consequently, 


or,  at  the  limit  as  A  T  approaches  zero, 

^. 
dt 


SATURATED    VAPOR 


Specific  Volume  of  Saturated  Vapor.  —  From  the  extreme 
difficulty  of  direct  experimental  determinations  of  the  specific 
volume  of  saturated  vapor  it  has  been  customary  to  compute  this 
property  by  aid  of  the  equation 


dt 

where  s  is  the  volume  of  the  vapor  and  o  is  the  volume  of  the 
liquid;  the  other  quantities  are  r  the  heat  of  vaporization,  T  the 

absolute   temperature,  —    the    mechanical    equivalent    of    heat, 

A 

and  -~  the  differential  coefficient  of  the  pressure  with  regard  to 

temperature.  A  close  approximation  to  the  differential  coefficient 
may  be  had  by  the  following  process:  choosing  a  temperature 
(for  example  100°  C.),  take  the  pressure  at  two  degrees  higher 
(102°  C.)  and  at  two  degrees  lower  (98°  C.)  and  divide  by  4. 
The  pressures  must  be  in  kilograms  per  square  meter.  From 
Table  III  we  deduce 


1109.3  ~  9i.    = 
A/  4 

The  pressures  are  1000  times  the  tabular  pressures  in  kilograms 
per  square  centimeter.     The   expression  -r*-  is  taken  to  represent 

an  operation  of  the  nature  explained  above. 

Equation  (107)  must  be  used  for  all  other  vapors  than  steam, 
and  for  steam  at  temperatures  less  than  100°  C.;  it  probably 
gives  the  best  values  for  the  specific  volume  of  steam  at  tem- 
peratures higher  than  100°  C.,  as  will  appear  in  the  discussion 
of  experimental  results. 

Specific  Volume  of  Saturated  Steam.  —  The  relation  of  the 
pressure  of  saturated  steam  to  the  temperature  is  given  by  Hoi- 
born  and  Henning  in  the  form  of  a  table  of  results  which  are 
quoted  directly  in  Table  III,  the  pressure  being  expressed  in 


SPECIFIC    VOLUME   OF    SATURATED    STEAM  91 

millimeters  of  mercury.     It  is  considered  that  the  best  way  of 

dealing  with  the  differential  coefficient  -*  is  to  replace  it  by  the 

dt 

ratio  — ,  using  4°  C.  for  the  interval  of  temperatures  A/. 

A  number  of  elements  enter  into  this  consideration.  If  the 
relation  of  the  pressure  to  the  temperature  could  be  represented 
by  a  second  degree  curve,  that  is,  if  such  a  curve  were  a  parabola 

with    its   axis   vertical,  the  ratio  — —  for  any  interval  would  be 

precisely  equal  to -p.      A  table  that  could  be  represented  by 

such  a  curve  would  have  constant  second  differences;  by  second 
differences  are  meant  the  differences  of  the  tabular  differences  as 
in  Table  III.  An  examination  of  second  differences  derived 
from  Table  III  shows  that  they  increase  slowly,  but  that  the 
increase  is  not  perceptible  for  four  degrees.  For  a  six-degree 
interval  the  increase  is  barely  perceptible,  and  for  ten  degrees 
it  is  very  apparent.  Now  the  precision  claimed  for  the  measure- 
ment of  temperature  is  TW  of  a  degree,  so  that  a  four-degree 
interval  appears  to  give  a  precision  of  computation  of  ^^  for  a 

single  value  of  — - .  It  may  be  noted  in  passing  that  the  pre- 
cision of  observation  of  the  height  of  the  mercury  column  is 
better  than  the  temperature  determinations  and  therefore  does 
not  contribute  to  the  probable  error. 

In  order  to  diminish  the  effect  of  local  variations  of  the  nature 

of  accidental  errors,  the  values  of  the  ratio  — ^-  were  computed  for 

z\/ 

each  degree  of  temperature  from  o°  C.  to  220°  C.  The  first  and 
second  differences  were  then  computed,  and  the  computed  values 

of  -^  were  changed  when  necessary  to  the  amount  of  yuW  in 

order  to  make  the  second  differences  regular.  This  process  is 
equivalent  to  drawing  a  smooth  or  fair  curve  to  represent  phys- 
ical properties  obtained  by  observation. 


02  SATURATED   VAPOR 

Having  values  of  the  ratio  — —  for  each  degree  of  temperature, 

the  specific  volumes  were  computed  by  equation  (107).  These 
values  were  then  tested  for  fairness  by  taking  second  differences, 
and  again  the  computed  values  were  varied  when  necessary  to 
the  extent  of  y^Vn  to  make  the  second  differences  regular.  The 
combined  effect  of  both  fairings  is  estimated  not  to  exceed  yj^ 
and  it  is  believed  that  the  probable  error  of  the  specific  volumes 
thus  determined  is  not  greater  than  that  amount  for  the  range 
of  temperature  50°  C.  to  200°  C.  covered  by  Holborn  and  Hen- 
ning's  experiments.  This  estimate  carries  with  it  the  assump- 
tion that  the  methods  of  fairing  give  somewhat  greater  mean 

A/> 
precision  than  can  be  attributed  to  a  single  computation  of    -rf- . 

For  the  range  of  temperature  from  o°  C.  to  50°  C.,  and  espe- 
cially for  temperatures  less  than  30°  C.  (86°  F.),  so  small  a 
probable  error  cannot  be  claimed  for  the  specific  volumes;  but 
that  range  has  less  interest  for  engineers.  For  temperatures  less 
than  30°  C.  the  specific  volumes  were  derived  in  the  following 
way.  In  the  first  place  the  values  Apu  given  in  Table  III  were 
computed  from  the  specific  volumes,  and  a  curve  was  drawn 
to  represent  them;  above  30°  C.  the  computed  values  varied  from 
the  curve  less  than  -gfa',  in  only  a  few  cases  was  the  variation 
greater  than  y^W  Below  30°  C.  it  was  considered  more  correct 
to  take  values  of  Apu  from  the  curve  which  was  there  ap- 
preciably straight,  and  values  of  the  specific  volume  were  ob- 
tained for  Table  III  by  inversion  of  the  method  of  computing 
Apu.  In  passing  it  may  be  said  that  all  values  of  Apu  in 
Tables  I  and  III  were  derived  from  the  curve  mentioned,  which 
gave  a  greater  degree  of  precision  than  needed  for  that  purpose. 

Since  the  pressures  corresponding  to  temperatures  above  200°  C. 
are  extrapolated,  .the  specific  volumes  computed  from  them  are 
affected  by  the  same  degree  of  uncertainty  that  attaches  to  the 
pressures. 

Specific  Volumes  of  Other  Vapors.  —  In  order  to  apply  equation 
(107)  to  the  computation  of  vapors  for  which  Regnault's  equations 


EXPERIMENTAL  DETERMINATIONS    OF  SPECIFIC   VOLUMES    93 


are  given  on  page  83,  we  may  derive  the  differential  coefficient 
in  the  form 


p   dt 


=  Aan 


The  following  table  gives  values  to  be  used  for  the  factors  that 
appear  in  that  equation. 


Sic 

e 

rN. 

Log  (A  a"). 

LogW). 

Alcohol  
Ether 

+ 

~ 

-    .1720041-0.0029143* 
-     3396624-0.0031223* 

-2.9992701-0.0590515* 
-4.4616396+0  0145775* 

Chloroform 

I 

-     3410130-0.0025856* 

-2.0667124-0  0131824* 

Carbon  bisulphide.. 
Carbon  tetrachloride 
Aceton  

: 

+ 

-    .4339778-0.0022372* 
-    .8611078-0.0002880* 
-    .3268535-0.0026148* 

-2.0511078-0.0088003* 
-1.3812195-0.0050220* 
-  1  .  9064582-  0  .  0215592  * 

,  temperature  C. 

Experimental   Determinations  of   Specific  Volumes.  —  By  far 

the  best  direct  determinations  of  the  specific  volumes  of  saturated 
steam  are  those  reported  by  Knoblauch,*  Linde,  and  Klebe  in 
connection  with  their  determinations  of  the  properties  of  super- 
heated steam.  These  experiments  determined  the  pressures  and 
temperature  at  constant  volume,  and  the  results  are  so  treated 
as  to  give  the  volume  at  saturation  by  extrapolation  with  great 
certainty.  In  their  report  they  claim  for  their  results,  including 
volumes  at  saturation,  a  probable  error  not  greater  than  yJT. 

COMPARISON  OF  EXPERIMENTAL  AND  COMPUTED  VALUES  OF  THE 
SPECIFIC    VOLUME    OF    SATURATED    STEAM. 


i 

Volume  Cu. 

M. 

1 

Volume  Cu. 

M. 

Tem- 

Tem- 

pera- 
ture. 

Experi- 
mental. 

Computed. 

Per  Cent 
Deviation. 

pera- 
ture. 

Experi- 
mental. 

Computed. 

Per  Cent 
Deviation. 

100 

1.674 

1.671 

+  0.18 

145 

0.4458 

0.4457 

+  0.02 

105 

1.421 

1.419 

+  0.14 

150 

0.3927 

0.3921 

+  0.15 

110 

1.211 

1.209 

+  0.17 

155 

0.3466 

0.3463 

+  0.09 

115 

1.036 

1.036 

0 

160 

0.3069 

0.3063 

+  0.20 

120 

0.8894 

0.8910 

-0.18 

165 

0.2724 

0.2729 

+  0.18 

125 

0.7688 

0.7698 

-0.13 

170 

0.2426 

0.2423 

+  0.12 

130 

0.6670 

0.6677 

-0.10 

175 

0.2168 

0.2164 

+  0.19 

135 

0.5809 

0.5812 

-0.05 

180 

0.1940 

0.1941 

-0.05 

140 

0  5080 

0  5081 

-0.02 

Mitleilungen  uber  Forschungsarbeiten,  etc.,  Heft  21,  S.  33,  1905. 


94 


SATURATED    VAPOR 


These  experimenters  give  32  determinations  of  the  volume  of 
saturated  steam.  In  order  to  make  a  comparison  of  these  experi- 
mental values  with  computations  in  Table  III,  a  large  plot  was 
made  with  temperatures  for  abscissae  and  logarithms  of  volumes 
for  ordinates,  and  a  fair  curve  was  drawn;  from  this  curve  the 
experimental  values  set  down  in  the  preceding  table  were  deduced; 
the  computed  values  are  taken  from  Table  III. 

The  greatest  deviation  is  0.2  of  one  per  cent,  which  is  the 
probable  error  assigned  by  the  experimenters  to  their  work.  It 
may  therefore  be  concluded  that  the  claim  of  a  probable  error 
not  in  excess  of  ^u  for  the  computed  values  of  the  specific  volume 
of  saturated  steam,  and  of  a  similar  degree  of  precision  for  the 
experimental  values,  is  warranted. 

Now  equation  (107)  includes  explicitly  the  heat  of  vaporiza- 
tion, the  absolute  temperature  and  the  mechanical  equivalent  of 

heat  as  well  as  the  differential  coefficient   — .     It  also  includes 

at 

the  heat  of  the  liquid  implicitly,  since  the  heat  of  vaporization 
is  derived  from  the  total  heat.  Consequently  the  claim  of  a 
precision  of  3^  for  the  specific  volume  attributes  a  like  degree 
of  precision  to  the  first  three  named  properties,  and  the  same 
effective  certainty  to  the  heat  of  the  liquid.  It  is  true  that  we 
may  independently  attribute  a  greater  precision  to  the  three 
first  properties  named.  Thus  a  probable  error  of  T<yV<r  is  claimed 
for  the  total  heat  by  Davis,  and  Callendar*  claims  a  prob- 
able error  of  ^Vtf  or  better  for  the  absolute  temperature;  the 
real  value  of  the  mechanical  equivalent  is  even  now  slightly  in 
question,  but  the  value  assigned  is  probably  in  error  less  than  TtfW. 

The  conclusion  appears  to  be  that  our  knowledge  of  the  prop- 
erties of  saturated  steam  is  sufficient  for  engineering  purposes, 
and  that  tables  computed  with  available  data  will  not  require 
change. 

Nature  of  the  Specific  Heats.  — In  the  application  of  the  gen- 
eral thermodynamic  method  on  page  86  the  term  h  is  intro- 
duced to  represent  the  specific  heat  of  saturated  steam,  and  there 
is  some  interest  in  the  determination  of  the  true  nature  of  this 

*  Phil.  Mag.,  Jan.,  1903. 


NATURE   OF  THE   SPECIFIC    HEATS 

property,  which  clearly  cannot  be  a  specific  heat  at  constant  pres- 
sure, nor  a  specific  heat  at  constant  volume,  since  both  pressure 
and  volume  change  with  the  temperature.  The  specific  heat  of 
the  liquid  c  properly  is  affected  by  the  same  consideration,  but 
as  the  increase  of  volume  is  small  and  is  neglected  in  thermo- 
dynamic  discussions,  the  importance  of  the  consideration  is  much 
less.  The  specific  heat  h  of  saturated  vapor  is  the  amount  of 
heat  necessary  to  raise  the  temperature  of  one  pound  of  the 
vapor  one  degree,  under  the  condition  that  the  pressure  shall 
increase  with  the  temperature,  according  to  the  law  for  saturated 
vapor. 

Equation  (105)  gives  a  ready  way  of  calculating  the  specific 
heat  for  a  vapor,  for  from  it 

,  dr        r 

k=C+^-T- 

Above  boiling-point  the  total  heat  of  water  may  be  expressed 
by  equation  (98),  page  81,  so  that  we  may  write 

r  =H  --  q=H  -     fcdt 
and 


dr  ^ 
dt  ~~  dt 


consequently 


7  0  ,. 

~di  "  r  =  *3745  "  °'OOI98  (*  - 

The  following  tables  give  a  few  values  of  h. 
SPECIFIC  HEAT  OF  SATURATED  STEAM. 


Temperature  C. 

IOO 

I25 

150 

I7S 

200 

Temperature  F. 

212 

257 

302 

347 

392 

Pressure,  pounds 

per  sq.  in. 

14.7 

33-7 

69.0 

129.4 

225.2 

Specific  heat  h 

—  I.O7O 

-  0.986 

-  o-9i5 

-  o-853 

-  0.804 

The  negative  sign  shows  that  heat  must  be  abstracted  from 
saturated  steam  when  the  temperature  and  pressure  are  increased, 
otherwise  it  will  become  superheated.  On  the  other  hand, 
steam,  when  it  suddenly  expands  with  a  loss  of  temperature  and 
pressure,  suffers  condensation,  and  the  heat  thus  liberated  sup- 
plies that  required  by  the  uncondensed  portion. 


SATURATED  VAPOR 

Hirn*  verified  this  conclusion  by  suddenly  expanding  steam  in 
a  cylinder  with  glass  sides,  whereupon  the  clear  saturated  steam 
suffered  partial  condensation,  as  indicated  by  the  formation  of  a 
cloud  of  mist.  The  reverse  of  this  experiment  showed  that  steam 
does  not  condense  with  sudden  compression,  as  shown  by  Cazin. 

Ether  has  a  positive  value  for  h.  As  the  theory  indicates,  a 
cloud  is  formed  during  sudden  compression,  but  not  during  sud- 
den expansion. 

The  table  of  values  of  h  for  steam  shows  a  notable  decrease 
for  higher  temperatures,  which  indicates  a  point  of  inversion  at 
which  h  is  zero  and  above  which  h  is  positive,  but  the  tempera- 
ture of  that  point  cannot  be  determined  from  our  experimental 
knowledge.  For  chloroform  the  point  of  inversion  was  calcu- 
lated by  Cazin f  to  be  i23°.48,  and  determined  experimentally  by 
him  to  be  between  125°  and  129°.  The  discrepancy  is  mostly 
due  to  the  imperfection  of  the  apparatus  used,  which  substituted 
finite  changes  of  considerable  magnitude  for  the  indefinitely 
small  changes  required  by  the  theory. 

Isothermal  Lines.  —  Since  the  pressure  of  saturated  vapor  is  a 
function  of  the  temperature  only,  the  isothermal  line  of  a  mixture 
of  a  liquid  and  its  vapor  is  a  line  of  constant  pressure,  parallel  to 
the  axis  of  volumes.  Steam  expanding  from  the  boiler  into  the 
cylinder  of  an  engine  follows  such  a  line;  that  is,  the  steam-line 
of  an  automatic  cut-off  engine  with  ample  ports  is  nearly  parallel 
to  the  atmospheric  line. 

The  heat  required  for  an  increase  of  volume  at  constant  pres- 
sure is 

Q  =r(x2  -*,) (108) 

in  which  r  is  the  heat  required  to  vaporize  one  pound  of  liquid 
and  xl  and  x.2  are  the  initial  and  final  qualities,  so  that  x2  —  ocl 
is  the  weight  of  liquid  vaporized. 

The  external  work  done  during  an  isothermal  expansion  is 

W=  p  (v2  -  vt)  =  pu  (x2  -  xj  .     .     .  (109) 

*  Bulletin  de  la  Societe  Ind.  de  Mulhouse,  cxxxiii. 
f  Comptes  rendus  de  I' Academic  des  Sciences,  Ixii. 


ISOENERGIC    OR   ISODYNAMIC    LINES  95 

Intrinsic  Energy.  —  Of  the  heat  required  to  raise  a  pound  of 
any  liquid  from  freezing-point  to  a  given  temperature  and  to 
completely  vaporize  it  at  that  temperature,  a  part  q  is  required 
to  increase  the  temperature,  another  part  p  is  required  to  change 
the  state  or  do  disgregation  work,  and  a  third  part  Apu  is  required 
to  do  the  external  work  of  vaporization.  Consequently  for  com- 
plete vaporization  we  may  have, 

Q  =  A(S  +  I  +  W)  =  q  +  p  +  Apu  =  H. 

For  partial  vaporization  the  heat  required  to  do  the  disgrega- 
tion work  will  be  xp,  and  the  heat  required  to  do  the  external 
work  will  be  Apxu.  Therefore  the  heat  required  to  raise  a  pound 
of  a  liquid  from  freezing-point  to  a  given  temperature  and  to 
vaporize  x  part  of  it  will  be 

Q  =  q  +  Xp  +  Apxu  =  A  (E  +  W) 

where  E  is  the  increase  of  intrinsic  energy  from  freezing-point. 
It  is  customary  to  consider  that 


(no) 


represents  the  intrinsic  energy  of  one  unit  of  weight  of  a  mixture 
of  a  liquid  and  its  vapor. 

Isoenergic  or  Isodynamic  Lines.  —  If  a  change  of  a  mixture 
of  a  liquid  and  its  vapor  takes  place  at  constant  intrinsic  energy, 
the  value  of  E  will  be  the  same  at  the  initial  and  final  conditions, 
and 

q2  —  ql  +  x2p2  —  x1p1  =  o       .     .     .     .(in) 


which  equation,  with  the  formulae 

v2  =  X2u2  +  o-;    vl  =  XjUi  +  a-    .     .     .     .    (112) 

enable  us  to  compute  the  initial  and  final  volumes.  If  desired, 
intermediate  volume  corresponding  to  intermediate  temperature 
can  be  computed  in  the  same  way,  and  a  curve  can  be  drawn 
in  the  usual  way  with  pressures  and  volumes  for  the  coordinates. 
For  example,  if  a  mixture  of  -fa  steam  and  -rV  water  expands 


96 


SATURATED   VAPOR 


isoenergically  from  100  pounds  absolute  to  15  pounds  absolute, 
the  final  condition  will  be 


Q-9  X  805.7  _ 

—  O.O  \QO. 
.2 

The  initial  and  final  specific  volumes  are 

vi  =  x\u\  +  a  =  °-9  (4-432  —  0.016)  +  0.016  =  3.990; 
v2  =  X2u2  +  o  =  0.9399  (26.28  —  0.016)  +  0.016  =  24.70. 

The  converse  problem  requiring  the  pressure  corresponding  to 
a  given  volume  cannot  be  solved  directly.  The  only  method 
of  solving  such  a  problem  is  to  assume  a  probable  final  pressure 
and  find  the  corresponding  volume;  then,  if  necessary,  assume 
a  new  final  pressure  larger  or  smaller  as  may  be  required,  and 
solve  for  the  volume  again;  and  so  on  until  the  desired  degree 
of  accuracy  is  obtained. 

This  method  does  not  give  an  explicit  equation  connecting  the 
pressures  and  volumes,  but  it  will  be  found  on  trial  that  a  curve, 
drawn  by  the  process  given  above  can  be  represented  fairly  well 
by  an  exponential  equation,  for  which  the  exponent  can  be 
determined  by  the  method  on  page  66. 

Having  given  or  determined  the  initial  and  final  volumes,  the 
exponential  equation  may  be  determined,  and  then  the  external 
work  may  be  calculated  by  the  equation 


n  —  i 

For  example,  the  exponent  for  the  equation  representing  the 
expansion  of  the  above  problem  is 

n  =  log  pi  —  log  p2  =      log  IPO  —  log  15        =  i 
log  v2  —  log  Vj.       log  24.70  —  log  3.990 

and  the  external  work  of  expansion  is 

w  _  ico  X  144  X  3.090  j  l  _  (249°  )-"'  |  _  100;8oo  ft..lbs. 
1.041  —  i  (          \24.o/        ) 


ENTROPY   OF   THE    LIQUID  97 

Since  there  is  no  change  in  the  intrinsic  energy  during  an 
isoenergic  expansion,  the  external  work  is  equivalent  to  the  heat 
applied.  Thus  in  the  example  just  solved  the  heat  applied  is 
equal  to 

100,000  -T-  778  =  130  B.T.U. 

There  is  little  occasion  for  the  use  of  the  method  just  given, 
which  is  fortunate,  as  it  is  not  convenient. 

Entropy  of  the  Liquid.  —  Suppose  that  a  unit  of  weight  of  a 
liquid  is  intimately  mingled  with  its  vapor,  so  that  its  tempera- 
ture is  always  the  same  as  that  of  the  vapor;  then  if  the  pressure 
of  the  vapor  is  increased  the  liquid  will  be  heated,  and  if  the 
vapor  expands  the  liquid  will  be  cooled.  So  far  as  the  unit  of 
weight  of  the  liquid  under  consideration  is  concerned,  the  pro- 
cesses are  reversible,  for  it  will  always  be  at  the  temperature  of 
the  substance  from  which  it  receives  or  to  which  it  imparts  heat, 
i.e.,  it  is  always  at  the  temperature  of  its  vapor. 

The  change  of  entropy  of  the  liquid  can  therefore  be  calculated 
by  equation  (37), 

d(f)  =  dQ 

which  may  here  be  written 


On  pa^ge  83  it  is  suggested  that  the  specific  heat  of  water  for 
temperature  Centigrade  may  be  expressed  as  follows : 

c  =  i  4-  k 

- ;    '.*•'•        \    -•-•} 

where  k  is  a  small  corrective  term  that  may  be  positive  or  negative 
as  the  case' may  be.  Using  this  correction,  equation  (113)  may 
be  written  VL 

ut 


98 


SATURATED    VAPOR 


The  first  term  can  readily  be  integrated  and  computed,  and  the 
second  term,  which  is  small,  can  be  determined  graphically,  so 
that  the  expression  for  entropy  of  water  becomes 


(n5) 


The  columns  of  entropy  of  water  in  the  tables  were  determined 
in  this  manner. 

In  jthe  discussion  of  entropy  on  page  31  it  was  pointed  out 
that  there  is  no  natural  zero  of  entropy  corresponding  to  the  abso- 
lute zero  of  temperature.  It  is  customary  to  treat  the  freezing- 
point  of  water  as  the  zero  of  entropy  both  for  that  liquid  and 
for  other  volatile  liquids;  some  liquids  therefore  have  negative 
entropies  at  temperatures  below  freezing-point  of  water  in  the 
appropriate  tables  of  their  properties. 

For  a  liquid  like  ether  which  has  the  heat  of  the  liquid  repre- 
sented by  an  empirical  equation, 

q  =  0.52901  t  +  0.0002959  ^2> 

the  specific  heat  is  first  obtained  by  differentiation,  giving 
c  —  0.52901  +  0.0005918  /. 

Then  the  increase  of  entropy  above  that  for  the  freezing-point  of 
water  may  be  obtained  by  aid  of  equation  (113),  which  gives  for 
ether  with  the  French  system  of  units, 

0=  I       ]  0.52901  +  0.0005918  (T  —  273)  {  —  ; 

«/273        (  )    1 

•'•     0=  J273    (0.3670  —  +  0.0005918  dt)', 

T 

.'.  0=  0.0005918  (T  -  273)  +  0.3670  log,  —  -  ; 

T 
.'.  0=  0.0005918  J  +  0.3670  log«  -  .....  (116) 


ENTROPY   OF   A    MIXTURE    OF   A   LIQUID  99 

For  temperatures  below  the  freezing-point  of  water,  equation 
(116)  gives  negative  numerical  results. 

Other  liquids  for  which  equations  for  the  heat  of  the  liquid 
are  given  on  page  83,  may  be  treated  in  a  similar  method. 

Entropy  due  to  Vaporization.  —  When  a  unit  of  weight  of  a 
liquid  is  vaporized  r  thermal  units,  equal  to  the  heat  of  vaporiza- 
tion, must  be  applied  at  constant  temperature.  Treating  such 
a  vaporization  as  a  reversible  process,  the  change  of  entropy  may 
be  calculated  by  the  equation 


This  property  is  given  in  the  "  Tables  for  Saturated  Steam," 
but  not  in  general  for  other  liquids. 

Entropy  of  a  Mixture  of  a  Liquid  and  its  Vapor.  —  The  increase 
in  entropy  due  to  heating  a  unit  of  weight  of  a  liquid  from  freez- 
ing-point to  the  temperature  /  and  then  vaporizing  x  portion  of 
it  is 

fi  .xr 

*  +  T, 

where  6  is  the  entropy  of  the  liquid,  r  is  the  heat  of  vaporization, 
and  T  is  the  absolute  temperature.     For  steam  —  may  be  taken 

from  the  tables;  for  other  vapors  it  must  usually  be  calculated. 

For  any  other  state  determined  by  x±  and  tl  we  shall  have,  for 
the  increase  of  entropy  above  that  of  liquid  at  freezing-point, 


The  change  of  entropy  in  passing  from  one  state  to  another 
is 

*-*t--f  +  0-^-*,    •    •    •  (117) 

When  the  condition  of  the  mixture  of  a  liquid  and  its  vapor 
is  given  by  the  pressure  and  value  of  x,  then  a  table  giving  the 
properties  at  each  pound  may  be  conveniently  used  for  this  work. 


IOO  SATURATED   VAPOR 

Adiabatic  Equation  for  a  Liquid  and  its  Vapor.  —  During  an 
adiabatic  change  the  entropy  is  constant,  so  that  equation  (117) 
gives 


When  the  initial  state,  determined  by  x1  and  tl  or  plt  is  known 
and  the  final  temperature  /2,  or  the  final  pressure  p2J  the  final 
value  x2  may  be  found  by  equation  (118).  The  initial  and  final 
volumes  may  be  calculated  by  the  equations 

^j  =  x^Ui  +  <r    and     v2  =  x2u2  -f  °"  .     .     .   (119) 

Tables  of  the  properties  of  saturated  vapor  commonly  give  the 
specific  volume  s1  but 

s  =  u  -\-  o-. 

The  value  of  <r  for  water  is  0,016,  and  for  other  liquids  will  be 
found  on  page  85. 

For  example,  one  pound  of  dry  steam  at  100  pounds  absolute 
pressure  will  have  the  values 

•JT  =  1.1273,      #1  =  o-4748,   xl  =  i. 

•*•  i 

If  the  final  pressure  is  15  pounds  absolute,  we  have 
-J  =  1.4409,      02  =0.3143; 

•*  2 

whence 

1.1273  +  0.4748  =  1.4409*2  +  0.3143; 

.*.  x2  =  0.894. 

The  initial  and  final  volumes  are 
^  =  sl  =  4.43 
v2  =  x2u2  +  o  =  23.5. 

Problems  in  which  the  initial  condition  and  the  final  tem- 
perature or  pressure  are  given  may  be  solved  directly  by  aid  of 
the  preceding  equations.  Those  giving  the  final  volume  instead 


ADIABATIC    EQUATION   FOR   A    LIQUID  ioi 

of  the  temperature  or  pressure  can  be  solved  only  by  approxi- 
mations. An  equation  to  an  adiabatic  curve  in  terms  of  p  and  v 
cannot  be  given/  but  such  a  curve  for  any  particular  case  may 
be  constructed  point  by  point. 

Clausius  and  Rankine  independently  and  at  about  the  same 
time  deduced  equations  identical  with  equations  (117)  and 
(118),  but  by  methods  each  of  which  differed  from  that  given 
here. 

Rankine  called  the  function 

xr 


the  thermodynamic  function  ;  Clausius  called  it  entropy. 

In  the  discussion  of  the  specific  heat  h  of  a  saturated  vapor,  it 
appeared  that  the  expansion  of  dry  saturated  steam  in  a  non- 
conducting cylinder  would  be  accompanied  by  partial  conden- 
sation. The  same  fact  may  be  brought  out  more  clearly  by  the 
above  problem. 

On  the  other  hand,  h  is  positive  for  ether,  and  partial  conden- 
sation takes  place  during  compression  in  a  non-conducting 
cylinder. 

For  example,  let  the  initial  condition  for  ether  be 

tl  =  10°  C  .,       rl  =  93.12,      0  =  0.0191,      xl  =  i, 
and  let  the  final  conditions  be 

*°  C.,      r2  =  72.26, 


then  '    •  +  0.0191  = 

283 

and 

Equation  (118)  applies  to  all  possible  mixtures  of  a  liquid  and 
its  vapor,  including  the  case  of  oct  =  o  or  the  case  of  liquid  with- 
out vapor,  but  at  the  pressure  corresponding  to  the  temperature 
according  to  the  law  of  saturated  vapor.  When  applied  to  hot 
water,  this  equation  shows  that  an  expansion  in  a  non-conduct- 
ing cylinder  is  accompanied  by  a  partial  vaporization. 


I02  SATURATED    VAPOR 

There  is  some  initial  state  of  the  mixture  such  that  the  value 
of  x  shall  be  the  same  at  the  beginning  and  at  the  end,  though  it 
may  vary  at  intermediate  states.  To  find  that  Value  make  x2  = 
xt  in  equation  (118)  and  solve  for  xlt  which  gives 


_ 
T         T 

±  2  •*  1 

The  value  of  xl  for  steam  to  fulfil  the  conditions  given  varies 
with  the  initial  and  final  temperatures  chosen,  but  in  any  case  it 
will  not  be  much  different  from  one  half.  It  may  therefore  be 
generally  stated  that  a  mixture  of  steam  and  water,  when 
expanded  in  a  non-conducting  cylinder,  will  show  partial  con- 
densation if  more  than  half  is  steam,  and  partial  evaporation  if 
more  than  half  water.  If  the  mixture  is  nearly  half  water  and 
half  steam,  the  change  must  be  investigated  to  determine  whether 
evaporation  or  condensation  will  occur;  but  in  any  case  the 
action  will  be  small. 

External  Work  during  Adiabatic  Expansion.  —  Since  no  heat 
is  transmitted  during  an  adiabatic  expansion,  all  of  the  intrinsic 
energy  lost  is  changed  into  external  work,  so  that,  by  equation 
(no), 

W  =  EI  —  E2  =    -  (ql  —  q2  +  x^  —  x^2)      .     .    (120) 


For  example,  the  external  work  of  one  pound  of  dry  steam  in 
expanding  adiabatically  from  100  pounds  to  15  pounds  absolute 
is 

W  =  778  (298.5  —  181.3  4-  i  X  805.7  —  0.894  X  896.2) 

W  =  121.7  X  778  =  94,700  foot-pounds. 

Attention  should  be  called  to  the  unavoidable  defect  of  this 
method  of  calculation  of  external  work  during  adiabatic  expan- 
sion, in  that  it  depends  on  taking  the  difference  of  quantities 
which  are  of  the  same  order  of  magnitude.  For  example,  the 
above  calculation  appears  to  give  four  places  of  significant  figures, 


EXTERNAL   WORK    DURING   ADIABATIC    EXPANSION     103 

while,  as  a  matter  of  fact,  the  total  heat  H  from  which  p  is  derived 
is  affected  by  a  probable  error  of  -  .  Both  the  quantities 

1000 

ql  +  xlPl  and  q2  +  X2p2 

have  a  numerical  value  somewhere  near  1000,  and  an  error  of 

-  is  nearly  equivalent  to  one  thermal  unit,  so  that  the  probable 
1000 

error  of  the  above  calculation  is  nearly  one  per  cent  For  a 
wider  range  of  temperature  the  error  is  less,  and  for  a  narrower 
range  it  is  of  course  larger.  This  matter  should  be  borne  in 
mind  in  considering  the  use  of  approximate  methods  of  calcula- 
tions; for  example,  the  temperature-  entropy  diagram  to  be  dis- 
cussed later. 

The  adiabatic  curve  cannot  be  well  represented  by  an  expo- 
nential equation;  for  if  an  exponent  be  determined  for  such  a 
curve  passing  through  points  representing  the  initial  and  final 
states,  it  will  be  found  that  the  exponent  will  vary  widely  with 
different  ranges  of  pressure,  and  still  more  with  different  initial 
values  of  x\  and  that,  further,  the  intermediate  points  will  not  be 
well  represented  by  such  an  exponential  curve  even  though  it 
passes  through  the  initial  and  final  points. 

This  fact  was  first  pointed  out  by  Zeuner,  who  found  that  the 
most  important  element  in  determining  n  was  xlt  the  initial  con- 
dition of  the  mixture.  He  gives  the  following  empirical  formula 
for  determining  n,  which  gives  a  fair  approximation  for  ordinary 
ranges  of  temperature  : 

n  =  1.035  + 


There  does  not  appear  to  be  any  good  reason  for  using  an 
exponential  equation  in  this  connection,  for  all  problems  can  be 
solved  by  the  method  given,  and  the  action  of  a  lagged  steam- 
engine  cylinder  is  far  from  being  adiabatic.  An  adiabatic  line 
drawn  on  an  indicator-diagram  is  instructive,  since  it  shows 
to  the  eye  the  difference  between  the  expansion  in  an  actual 
engine  and  that  of  an  ideal  non-conducting  cylinder;  but  it  can 


104 


SATURATED  VAPOR 


be  intelligently  drawn  only  after  an  elaborate  engine  test.  For 
general  purposes  the  hyperbola  is  the  best  curve  for  comparison 
with  the  expansion  curve  of  an  indicator-diagram,  for  the  reason 
that  it  is  the  conventional  curve,  and  is  near  enough  to  the  curve 
of  the  diagrams  from  good  engines  to  allow  a  practical  engineer 
to  guess  at  the  probable  behavior  of  an  engine,  from  the  diagram 
alone.  It  cannot  in  any  sense  be  considered  as  the  theoretical 
curve. 

Temperature-Entropy  Diagram.  —  If  the  entropies  of  the 
liquid  and  the  entropies  of  vaporization  for  steam  are  plotted  with 
temperature  for  ordinates  we  get  a  diagram  like  3oa;  very  com- 

monly absolute  temperatures 
are  taken  in  drawing  the  dia- 
gram in  order  to  emphasize 
the  role  played  by  absolute 
temperatures  in  the  deter- 
mination of  the  efficiency  of 
Carnot  's  cycle.  It  would  seem 
better  to  take  the  temperature 
by  the  centigrade  or  the  Fah- 
FlG.3oa.  renheit  thermometer,  as  they 

are  the  basis  of  steam-tables, 

and  the  temperature-  entropy  diagram  is  the  equivalent  of  such  a 
table. 

Now  the  entropy  of  a  mixture  containing  x  part  steam  is 


0.1     0.2     0.3     O.i     0.5     0.6     0.7      0.8      0.9 


so  that  the  entropy  of  a  mixture  containing  x  part  of  steam  can 
be  determined  by  dividing  the  line  such  as  de  (which  represents 
the  entropy  of  vaporization)  in  the  proper  ratio. 


dc 


It  is  convenient  to  divide  the  several  lines  like  ab  and  de  into 
tenths  and  hundredths,  and  then,  if  an  adiabatic  expansion  is 


TEMPERATURE-ENTROPY    DIAGRAM  105 

represented  by  a  vertical  line  like  be,  the  entropy  at  c  may  be 
determined  by  inspection  of  the  diagram.  Conversely,  by  noting 
the  temperature  at  which  a  given  line  of  constant  entropy  crosses 
a  line  of  given  quality  we  may  determine  the  temperature  to 
which  it  is  necessary  to  expand  to  attain  that  quality,  a  determina- 
tion which  cannot  be  made  directly  by  the  equation. 

When  a  temperature- entropy  diagram  is  used  as  a  substitute 
f or  a  "  Table  of  the  Properties  of  Saturated  Steam,"  it  is  custom- 
ary to  draw  the  lines  of  constant  quality  or  dryness  factor,  and 
other  lines  like  constant  volume  lines  and  lines  of  constant  heat 
contents  or  values  of  the  expression 

ocr  +  q, 

the  use  of  which  will  appear  in  the  discussion  of  steam-engines 
and  steam-turbines. 

To  get  a  series  of  constant  volume  lines  we  may  compute  the 
volume  for  each  quality  oc1  =  .ilt  x2  =  .2,  x  =  .3,  etc.,  by  the 
equation 

•u  =  ocu  +  tr} 

'and  since  the  volume  increases  proportionally  to  the  increase  in 
x,  we  may  readily  determine  the  points  on  that  line  for  which 
the  volume  shall  be  whole  units,  such  as  2  cubic  feet,  3  cubic  feet, 
etc.  Points  for  which  the  volumes  are  equal  may  now  be  con- 
nected by  fair  curves,  so  that  for  any  temperature  and  entropy  the 
volume  may  readily  be  estimated. 

Curves  of  equal  heat  contents  can  be  constructed  in  a  similar 
way. 

If  desired,  a  curve  of  temperatures  and  pressures  can  be  drawn 
so  that  many  problems  can  be  solved  approximately  by  aid  of  the 
compound  diagram. 

At  the  back  of  this  book  a  temperature-entropy  diagram  will 
be  found  which  gives  the  properties  of  saturated  and  superheated 
steam.  It  is  provided  with  a  scale  of  temperatures  at  either 
side,  and  a  scale  of  entropies  at  the  bottom,  while  there  is  a  scale 
of  pressure  at  the  right. 


I06  SATURATED   VAPOR 

To  solve  a  problem  like  that  on  page  100,  i.e.,  to  find  the  quality 
after  an  adiabatic  expansion  from  100  pounds  absolute  to  15 
pounds  absolute,  and  the  specific  volume  at  the  initial  and  final 
states,  proceed  as  follows: 

From  the  curve  of  temperatures  and  pressures,  select  the  tem- 
perature line  which  corresponds  to  100  pounds  and  note  where  it 
cuts  the  saturation  curve,  because  it  is  assumed  that  the  steam  is 
initially  dry.  The  diagram  gives  the  entropy  as  approximately 
i  .61.  Note  the  temperature  line  which  cuts  the  temperature- 
pressure  curve  at  1 5  pounds,  and  estimate  the  value  of  x  from  its 
intersection  with  the  entropy  line  1.6 1;  by  this  method  the  value 
of  x  is  found  to  be  about  0.89.  In  like  manner  the  volume  may 
be  estimated  to  be  about  23.4  cubic  feet. 

Temperature-Entropy  Table.  —  Now  that  the  computation  of 
isoentropic  changes  has  ceased  to  be  the  diversion  of  students 
of  theoretical  investigations  and  has  become  the  necessity  of 
engineers  who  are  engaged  in  such  matters  as  the  design  of 
steam-turbines,  the  somewhat  inconvenient  methods  which  were 
incapable  of  inverse  solutions,  have  become  somewhat  burden- 
some. A  remedy  has  been  sought  in  the  use  of  temperature- 
entropy  diagrams  just  described.  Such  a  diagram  to  be  really 
useful  in  practice  must  be  drawn  on  so  large  a  scale  as  to  be  very 
inconvenient,  and  even  then  is  liable  to  lack  accuracy.  To  meet 
this  condition  of  affairs  a  temperature- entropy  table  has  been  com- 
puted and  added  to  the  "  Tables  of  the  Properties  of  Saturated 
Steam."  In  this  table  each  degree  Fahrenheit  from  180°  to  430° 
is  entered  together  with  the  corresponding  pressure.  There 
have  been  computed  and  entered  in  the  proper  columns  the 
following  quantities,  namely,  quality  x,  heat  contents  xr  +  q,  and 
specific  volume  v,  for  each  hundredth  of  a  unit  of  entropy. 

In  the  use  of  this  table  it  is  recommended  to  take  the  nearest 
degree  of  temperature  corresponding  to  the  absolute  pressure 
if  pressures  are  given.  Following  the  line  across  the  table  select 
that  column  of  entropy  which  corresponds  most  nearly  with  the 
initial  condition;  the  corresponding  initial  volume  may  be  read 
directly.  Follow  down  the  entropy  column  to  the  lower  temper- 


TEMPERATURE-ENTROPY   TABLE  107 

ature  and  then  find  the  value  of  x  and  the  specific  volume.  The 
external  work  for  adiabatic  expansion  may  now  readily  be  found 
by  aid  of  equation  (120),  page  102.  As  will  appear  later,  the 
problems  that  arise  in  practice  usually  require  the  heat  contents 
and  not  the  intrinsic  energy,  so  that  property  has  been  chosen 
in  making  up  the  table. 

For  example,  the  nearest  temperature  to  100  pounds  per  square 
inch  is  328°  F.;  the  entropy  column  1.59  gives  for  x,  0.995,  which 
indicates  half  of  one  per  cent  of  moisture  in  the  steam.  The  corre- 
sponding volume  is  4.39  cubic  feet.  The  nearest  temperature  to 
15  pounds  absolute  is  213°  F.,  and  at  1.59  entropy  the  quality 
is  0.888  and  the  specific  volume  corresponding  is  23.2  cubic 
feet. 

If  greater  accuracy  is  desired  we  must  resort  to  interpolation. 
Usually  it  will  be  sufficient  to  interpolate  between  the  lines  for 
temperature  in  a  given  column  of  entropy,  because  the  quantity 
that  must  be  determined  accurately  is  usually  the  difference 

x1rl  +  ql  —  (x2r2  +  q2) 

and  this  difference  for  two  given  temperatures  tl  and  /2  is  very 
nearly  the  same  if  taken  out  of  two  adjacent  entropy  columns. 
A  similar  result  will  be  found  for  the  difference 

XlPl    +    01   -     (*2/>2    +    fc), 

if  computed  for  values  of  x  found  in  adjacent  columns. 

Another  way  of  looking  at  this  matter  is  that  one  hundredth 
of  a  unit  of  entropy  at  330  pounds  corresponds  to  one  per  cent 
of  moisture. 

Evidently  this  table  can  be  used  to  solve  problems  in  which 
the  final  volumes  are  given,  or,  as  will  appear  later,  to  determine 
intermediate  pressures  for  steam-turbines. 


I08  SATURATED   VAPOR 

EXAMPLES. 

1.  Water  at  100°  F.  is  fed  to  a  boiler  in  which  the  pressure  is 
120  pounds  absolute  per  square  inch.     How  much  heat  must 
be  supplied  to  evaporate  each  pound?    Ans.  1121.2  B.T.U. 

2.  One  pound  wet  steam  at  150  pounds  absolute  occupies  2.5 
cubic  feet.     What  per  cent  of  moisture  is  present?    What  is  the 
"quality"  of  the  steam?    Ans.  17.05  per  cent  of  moisture  x  = 
0.8295. 

3.  A  pound  of  steam  and  water  at  150  pounds  pressure  is 
0.6  steam.     What  is  the  increase  of  entropy  above  that  of  water  at 
32°  F.?    Ans.  1.1473. 

4.  A  kilogram  of  chloroform  at  100°  C.  is  0.8  vapor.     What  is 
the  increase  of  entropy  above  that  of  the  liquid  at  o°  C.  ?    Ans. 
0.1959. 

5.  The  initial  condition  of  a  mixture  of  water  and  steam  is 
t  =  320°  F.,  x  =0.8.     What  is  the  final  condition  after  adiabatic 
expansion  to  212°  F.  ?    Ans.  0.74. 

6.  The  initial  condition  of  a  mixture  of  steam  and  water  is  p  = 
3000  mm.,  x  =0.9.     Find  the  condition  after  an  adiabatic  expan- 
sion to  600  mm.     Ans.  0.830. 

7.  A  cubic  foot  of  a  mixture  of  water  and  steam,  x  =  0.8,  is 
under  the  pressure  of  60  pounds  by  the  gauge.     Find  its  volume 
after  it  expands  adiabatically  till  the  pressure  is  reduced  to  10 
pounds  by  the  gauge;  also  the  external  work  of  expansion.     Ans. 
2.69  cubic  feet  and  10,000  foot-pounds. 

8.  Three  pounds  of  a  mixture  of  steam  and  water  at   120 
pounds   absolute  pressure   occupy   4.5   cubic  feet.     How   much 
heat  must  be  added  to  double  the  volume  at  the  same  pressure, 
and  what  is  the  change  of  intrinsic  energy?    Ans.  1065  B.T.U. ; 
750,100  foot-pounds. 

9.  Find   the   intrinsic   energy,   heat  contents   and   volume   of 
5  pounds  of  a  mixture  of  water  and  steam  which  is  80  per  cent 
steam,  the  pressure  being  150  pounds  absolute.     Ans.  Intrinsic 
energy,  3,709,000;  heat  contents,  5102  B.T.U.;  volume,  12.1  cubic 
feet. 


TEMPERATURE-ENTROPY  TABLE  109 

10.  Three  pounds  of  water  are  heated  from  60°  F.  and  evapo- 
rated under  135.3  pounds  gauge  pressure.     Find  the  heat  added, 
and   the   changes   in  volume,  and  intrinsic  energy.     Ans.  Heat 
added,  3498  B.T.U.;   increase  in  volume,  9.00  cubic  feet;   intrinsic 
energy,  2,530,000. 

11.  A  pound  of  steam  at  337°-7  F.   and   100  pounds  gauge 
pressure  occupies  3  cubic  feet.     Find  its  intrinsic  energy  and  its 
entropy  above  32°  F.     Ans.  Intrinsic  energy,  718,000;    entropy, 

I-338. 

12.  Two  pipes  deliver  water  into  a  third.     One  supplies  300 
gallons  per  minute  at  70°  F. ;   the  other,  90  gallons  per  minute  at 
200°  F.     What   is   the   temperature   of  the  water  after  the  two 
streams  unite  ?    Ans.  ioo°.i  F. 

13.  A  test  of  an  engine  with  the  cut-off  at  0.106  of  the  stroke, 
and  the  release  at  0.98  of  the  stroke,  and  with  4.5  per  cent  clear- 
ance, gave  for  the  pressure  at  cut-off  62.2  pounds  by  the  indicator, 
and  at  release  6.2  pounds;  the  mixture  in  the  cylinder  at  cut-off 
was  0.465  steam,  and  at  release  0.921  steam.     Find  (i)  condition 
of  the  mixture  in  the  cylinder  at  release  on  the  assumption  of 
adiabatic  expansion  to  release;    (2)  condition  of  mixture  on  the 
assumption  of  hyperbolic  expansion,  or  that  pv  =  p^\    (3)  the 
exponent  of  an  exponential  curve  passing  through  points  of  cut- 
off and  release;   (4)  exponent  of  a  curve  passing  through  the  initial 
and  final  points  on  the  assumption  of  adiabatic  expansion;    (5) 
the  piston  displacement  was  0.7  cubic  feet,  find  the  external  work 
under  exponential  curve  passing  through  the  points  of  cut-off  and 
release;    also   under   the  adiabatic  curve.     Ans.   (i)  0.473;    (2) 
o-53°;   (3)  n  =  0.6802;   (4)  n  =  1.0565;   (5)  3093  and  2130  foot- 
pounds. 


CHAPTER  VII. 

SUPERHEATED    VAPORS. 

A  DRY  and  saturated  vapor,  not  in  contact  with  the  liquid 
from  which  it  is  formed,  may  be  heated  to  a  temperature  greater 
than  that  corresponding  to  the  given  pressure  for  the  same 
vapor  when  saturated;  such  a  vapor  is  said  to  be  superheated. 
When  far  removed  from  the  temperature  of  saturation,  such  a 
vapor  follows  the  laws  of  perfect  gases  very  nearly,  but  near  the 
temperature  of  saturation  the  departure  from  those  laws  is  too 
great  to  allow  of  calculations  by  them  for  engineering  purposes. 

All  the  characteristic  equations  that  have  been  proposed, 
have  been  derived  from  the  equation 

.  pv  =  RT, 

which  is  very  nearly  true  for  the  so-called  perfect  gases  at  mod- 
erate temperatures  and  pressures;  it  is,  however,  well  known 
that  the  equation  does  not  give  satisfactory  results  at  very  high 
pressures  or  very  low  temperatures.  To  adapt  this  equation  to 
represent  superheated  steam,  a  corrective  term  is  added  to  the 
right-hand  side,  which  may  most  conveniently  be  assumed  to 
be  a  function  of  the  temperature  and  pressure,  so  that  calcula- 
tions by  it  may  be  made  to  join  on  to  those  for  saturated  steam. 

The  most  satisfactory  characteristic  equation  of  this  sort  is 
that  given  by  Knoblauch,*  Linde,  and  Klebe, 


pv  =  BT  -  p  (i  +  ap)    c  -D       -     -   (121) 

in  it  the  pressure  is  in  kilograms    per  square  metre,  v  is  in 
cubic    metres,    and    T    is    the    absolute    temperature   by    the 

*  Mitteilungen  uber  Forschungsarbeiten,  etc.,  Heft  21,  S.  33,  1905. 

no 


SUPERHEATED    VAPORS  III 

centigrade    thermometer.     The    constants    have    the    following 
values  : 

B  =•  47.10,       a  =  0.000002,       C  =  0.031,       D  —  0.0052. 

In  the  English  system  of  units,  the  pressures  being  in  pounds 
per  square  foot,  the  volumes  in  cubic  feet  per  pound,  and  the 
temperatures  on  the  Fahrenheit  scale,  we  have 

^  =  85.85  r-^(i+o.ooooo976/>)(l50>y000-  0.0833)     (122) 

The  following  equation  may  be  used  with  the  pressure  in 
pounds  per  square  inch  : 


^  =  0.5962  T-p  (i  +0.0014  P)(^jr^~  0.0833)     •   (123) 

The  labor  of  calculation  is  principally  in  reducing  the  cor- 
rective term,  and  especially  in  the  computation  of  the  factor 
containing  the  temperature.  A  table  on  page  112  gives  values 
of  this  factor  for  each  five  degrees  from  100°  to  600°  F.;  the 
maximum  variation  in  the  calculation  of  volume  by  aid  of  the 
table  without  interpolation  is  about  0.4  of  one  per  cent  at  336 
pounds  pressure  and  428°  F.  ;  that  is  at  the  upper  limit  of  our 
table  for  saturated  steam.  At  150  pounds  and  358°  F.,  which  is 
about  the  middle  range  of  our  table  for  saturated  steam,  the  vari- 
ation is  not  more  than  0.2  of  one  per  cent,  which  is  not  greater 
than  the  probable  error  of  the  equation  itself  under  those  con- 
ditions. At  lower  pressures  and  at  higher  temperatures  the  error 
tends  to  diminish.  Exact  results  can  be  had  at  all  temperatures 
by  interpolation  in  the  table. 

Knoblauch  attributes  to  his  equation  a  probable  error  of  0.2  of  a 
per  cent  within  the  range  of  his  experiments  which  extends  from 
100°  C.  to  180°  C.,  and  to  about  50°  C.  of  superheating.  It  has 
been  shown  that  a  special  treatment  of  his  experimental  values 
extrapolated  to  saturation  shows  at  no  place  a  greater  discrepancy 
from  the  tabular  values  of  Table  III  than  0.2  of  a  per  cent.  His 
equation  is  nearly  as  good,  the  maximum  discrepancy  within  his 


112 


SUPERHEATED   VAPORS 


range  being  one-third  of  a  per  cent  at  160°  C.  Below  boiling- 
point  the  greatest  discrepancy  of  his  equation  is  half  a  per  cent  at 
50°  C. ;  toward  freezing-point  the  decrepancy  decreases  to  zero. 


TABLE   I. 


Values  of  the  factor  Ls°'3°^>oo°  __  0.0833. 


Temperature. 

Value 
of 
Factor. 

Temperature. 

Value 
of 
Factor. 

Temperature. 

Value 
of 
Factor. 

Temperature. 

Value 
of 
Factor. 

Fahr. 

Abs. 

Fahr. 

Abs. 

Fahr. 

Abs. 

Fahr. 

Abs. 

2OO 

659-5 

0.441 

300 

759-5 

0.260 

400 

859.5 

0-153 

500 

959-5 

0.087 

205 

664.5 

0.429 

305 

764-5 

0-253 

405 

864.5 

0.149 

505 

964-5 

0.084 

210 

669.5 

0.417 

310 

769-5 

0.247 

410 

869.5 

0.145 

510 

969-5 

0.083 

215 

674.5 

0.405 

315 

774-5 

0.240 

415 

874.5 

o.  141 

515 

974.5 

0.079 

22O 

679-5 

o-395 

320 

779-5 

0.234 

420 

879.5 

0.138 

520 

979-5 

0.077 

225 

684.5 

0.385 

325 

784.5 

0.228 

425 

884.5 

0.134 

525 

984-5 

0.074 

230 

689-5 

o-375 

33° 

789-5 

0.222 

43° 

889.  < 

0.131 

53° 

989.5 

0.072 

235 

694.5 

0.365 

335 

794-5 

0.216 

435 

894.5 

o.  127 

535 

994-5 

0.070 

240 

699-5 

0-356 

340 

799-5 

0.2II 

440 

899.5 

0.123 

540 

999.5 

0.067 

245 

704.5 

o-347 

345 

804.5 

0.205 

445 

904.5 

O.  120 

545 

1004.5 

0.065 

250 

7°9-5 

0-338 

35° 

809.5 

0.2OO 

45° 

909.5 

o.  117 

55° 

1009.5 

0.063 

255 

714.5 

0.329 

355 

814.5 

0.195 

455 

914.5 

O.II3 

555 

1014.5 

0.061 

260 

7I9.5 

0.320 

360 

819.5 

o.  190 

460 

9I9.5 

O.  110 

560 

1019.5 

0.059 

265 

724-5 

0.312 

365 

824.5 

0-185 

465 

924.5 

o.  107 

565 

1024.5 

0.057 

270 

729-5 

0.304 

37° 

829.5 

O.lSo 

47° 

929-5 

o.  104 

57o 

1029.5 

0-055 

275 

734-5 

o.  296 

375 

834.5 

0-175 

475 

934-5 

0.  101 

575 

1034-5 

0.053 

280 

739-5 

0.288 

380 

839.5 

O.I7I 

480 

939-5 

0.098 

580 

i°39  -5 

0.051 

585 

744-5 

0.281 

385 

844-5 

0.166 

485 

944-5 

0.095 

585 

1044.5 

0.049 

290 

749-5 

0.274 

390 

849-5 

o.  162 

490 

949-5 

0.092 

590 

1049-5 

0.047 

295 

754-5 

0.267 

395 

854.5 

0.158 

495 

954-5 

0.090 

595 

1054-5 

0.045 

Specific  Heat.  —  Two  investigations  have  been  made  of  the 
specific  heat  of  superheated  steam  at  constant  pressure,  one  by 
Professor  Knoblauch*  and  Dr.  Jakob  and  the  other  by  Pro- 
fessor Thomas  and  Mr.  Short ;  f  the  results  of  the  latter 's  inves- 
tigation have  been  communicated  for  use  in  this  book  in 
anticipation  of  the  publication  of  the  completed  report. 

*  Mitteilungen  ubcr  Forschungsarbeiten,  Heft  36,  p.  109. 
f  Thesis  by  Mr.  Short,  Cornell  University 


SPECIFIC    HEAT 


Professor  Knoblauch's  report  gives  the  results  of  the  inves- 
tigations made  under  his  direction  in  the  form  of  a  table  giving 
specific  heats  at  various  temperatures  and  pressures  and  in  a 
diagram,  which  can  be  found  in  the  original  memoir,  and  he 
also  gives  a  table  of  mean  specific  heats  from  the  temperature  of 
saturation  to  various  temperatures  at  several  pressures.  This 
latter  table  is  given  here  in  both  the  metric  system  and  in  the 
English  system  of  units. 

SPECIFIC   HEAT   OF   SUPERHEATED   STEAM. 

Knoblauch  and  Jakob 


/KgperSqCm 

1 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

P  Lbs  per  Sq  In. 

14.2 

28.4 

56.9 

85.3 

113.8 

142.2 

170.6 

199.1 

227.5 

156.0 

284.4 

t»  Cent. 

99° 

120° 

143° 

158° 

169° 

179° 

187° 

194° 

200° 

206° 

211° 

t»  Fahr. 

210° 

248° 

289° 

3i6° 

336° 

350° 

368° 

381° 

392° 

403° 

412° 

Fahr. 

Cent. 

212° 

100° 

O    4.6"? 

*02° 

ISO0 

w  •  T^O 

o  4.62 

o  478 

O    <Jl  S 

3^* 
392° 

200° 

v/  •  t+\J& 

0.462 

W  »  £}  ^  (J 

o-475 

w*  j  -1  j 
0.502 

0-53° 

0.560 

o-597 

0'635 

0.677 

.  .  . 

.  .  . 

.  .  . 

482° 

250° 

0.463 

0.474 

0.495 

0.514 

0-532 

o.552 

0.570 

0.588 

0.609 

0-635 

0.664 

572° 

300° 

0.464 

°-475 

0.492 

0-505 

0.517 

0.530 

0.541 

0.550 

0.561 

0.572 

0.585 

662° 

350° 

0.468 

0.477 

0.492 

0-503 

0.512 

0.522 

0.529 

0.536 

0-543 

0-55° 

0-557 

752° 

400° 

°-473 

0.481 

0.494 

0.504 

0.512 

0.520 

0.526 

0-531 

0-537 

0.542 

0-547 

The  construction  of  this  table  is  readily  understood  from  the 
following  example:  —  Required  the  heat  needed  to  superheat  a 
kilogram  of  steam  at  4  kilograms  per  square  centimetre  from 
saturation  to  300°  C.  The  saturation  temperature  (to  the  nearest 
degree)  is  143°  C.;  so  that  the  steam  at  300°  is  superheated  157°, 
and  for  this  is  required  the  heat 

157  X  0.492  =  77.2  calories. 

The  experiments  of  Professor  Knoblauch  were  made  at  2,  4, 
6,  and  8  kilograms  per  square  centimetre;  the  remainder  of  the 
table  was  obtained  from  the  diagram  which  was  extended  by  aid 
of  a  diagram  to  the  extent  indicated.  Within  the  limits  of  the 
experimental  work  the  table  may*  be  used  with  confidence;  the 
greatest  error  being  probably  not  more  than  one-third  of  one  per 
cent. 


H4 


SUPERHEATED  VAPORS 


The  following  table  gives  the  mean  specific  heat  of  super- 
heated steam  as  measured  on  a  facsimile  of  Professor  Thomas's 
original  diagram  without  exterpolation. 


SPECIFIC   HEAT   OF   SUPERHEATED   STEAM 

Thomas  and  Short. 


Pressure  Lbs.  per  Sq.  In.     (Absolute.) 

Degrees  of 

Superheat  Fahr. 

6 

15 

30 

50 

100 

200 

400 

20° 

0.536 

°-S47 

0.558 

0-571 

0.593 

0.621 

0.649 

50° 

0.522 

0-532 

0.542 

0-555 

0.575 

0.600 

0.621 

100° 

°-5°3 

0.512 

0.524 

0-537 

0.557 

0.581 

o-599 

150° 

0.486 

0.496 

0.508 

0.522 

0.544 

0.567 

0-585 

200° 

0.471 

0.480 

0.494 

0.509 

0-533 

0.556 

0-574 

250° 

0.456 

o.  466 

0.481 

0.496 

0.522 

0.546 

0.564 

300° 

0.442 

°-453 

0.468 

0.484 

0.511 

0-537 

0-554 

Here  again  the  arrangement  of  the  table  can  be  made  evident 
by  an  example :  —  Required  the  heat  needed  to  superheat  steam 
100  degrees  at  200  pounds  per  square  inch  absolute.  The  mean 
specific  heat  from  saturation  is  0.581,  so  that  the  heat  required 
is  58.1  thermal  units. 

Total  Heat.  —  In  the  solution  of  problems  that  arise  in  engi- 
neering it  is  convenient  to  use  the  total  amount  of  heat  required 
to  raise  one  pound  of  water  from  freezing-point  to  the  tempera- 
ture of  saturated  steam  at  the  given  pressure  and  to  vaporize 
it  and  to  superheat  it  at  that  pressure  to  the  given  temperature. 
This  total  heat  may  be  represented  by  the  expression 

HSup.  =  q  +  r  +  cp  (/-/,) 

where  /  is  the  superheated  temperature  of  the  superheated 
steam,  tt  is  the  temperature  of  saturated  steam  at  the  given 
pressure  p,  and  q  and  r  are  the  corresponding  heat  of  the  liquid 
and  heat  of  vaporization.  The  mean  specific  heat  cp  may 
usually  be  selected  from  one  of  the  given  tables  without  inter- 


ENTROPY 

polation,  as  a  small  variation  does  not  have  a  very  large 
effect. 

The  total  heat  or  heat  contents  of  superheated  steam  in  thfe 
temperature- entropy  table  were  obtained  by  the  following 
method.  From  Professor  Thomas's  diagram  giving  mean 
specific  heats,  curves  of  specific  heats  at  various  temperatures 
and  at  a  given  pressure  were  obtained,  and  the  curves  thus 
obtained  were  faired  after  a  comparison  with  curves  constructed 
with  Professor  Knoblauch 's  specific  heats  at  those  temperatures. 
These  curves  were  then  integrated  graphically  and  the  results 
checked  by  comparison  with  his  mean  specific  heats. 

Entropy.  —  By  the  entropy  of  superheated  steam  is  meant 
the  increase  of  entropy  due  to  heating  water  from  freezing-point 
to  the  temperature  of  saturated  steam  at  the  given  pressure,  to 
the  vaporization  and  to  the  superheating  at  that  pressure.  This 
operation  may  be  represented  as  follows: 

e  +  —  +  fr  Cpdt 

Ts       JT.     T 

in  which  T  is  the  absolute  temperature  of  the  superheated  steam, 
and  Tt  is  the  temperature  of  the  saturated  steam  at  the  given 

pressure;  6  and—  may  be  taken  from  the  "  Tables  of  Saturated 

J-  s 

Steam."  The  last  term  was  obtained  for  the  temperature- 
entropy  table  by  graphical  integration  of  curves  plotted 

with  values  of  -*  derived    from  the  curves  of  specific  heats  at 

various  temperatures  just  described  under  the  previous  section. 

If  the  temperature- entropy  table  is  not  at  hand,  the  last  term 
of  the  above  expression  may  be  obtained  approximately  by  divid- 
ing the  heat  of  superheating,  by  the  mean  absolute  temperature 
of  superheating. 

This  may  be  expressed  as  follows: 


4r  (/  +  O   +  459-5 


SUPERHEATED   VAPORS 

where  /  is  the  temperature  of  the  superheated  steam,  ts  is  the 
temperature  of  saturated  steam  at  the  given  pressure,  and  cp  is 
the  mean  specific  heat  of  superheated  steam. 

If  this  method  is  considered  to  be  too  crude,  the  computation 
can  be  broken  into  two  or  more  parts.  Thus  if  /t  is  an  inter- 
mediate temperature,  the  increase  of  entropy  due  to  superheat- 
ing may  be  computed  as  follows: 

cv'  (t,  -  Q      .      c,"  (t  -  /,)  -  c0'  (t,  -  Q 
i  (/!  +  O  +  459-5  4  (t  +  *i)  +  459-5 

where  cpr  is  the  mean  specific  heat  between  /,  and  tv  and  cpn  is 
the  specific  heat  between  4  and  t.  This  method  may  evidently 
be  extended  to  take  in  two  intermediate  temperatures  and  give 
three  terms. 

Adiabatic  Expansion.  —  The  treatment  of  superheated  steam 
in  this  chapter  resembles  that  for  saturated  steam  hi  that  it  does 
not  yield  an  explicit  equation  for  the  adiabatic  line.  If  the 
steam  were  strongly  superheated  during  the  whole  operation  it 
is  probable  that  the  adiabatic  line  would  be  well  represented 
by  an  exponential  equation,  and  for  such  case  a  mean  value  of 
the  exponent  could  be  determined  that  would  suffice  for  engi- 
neering work.  But  even  with  strongly  superheated  steam  at 
the  initial  condition  the  final  condition  is  likely  to  show  moisture 
in  the  steam  after  adiabatic  expansion,  or,  for  that  matter,  after 
expansion  of  the  steam  in  the  cylinder  of  an  engine  or  in  a  steam- 
turbine. 

Problems  involving  adiabatic  expansion  of  steam  which  is 
initially  superheated  can  be  solved  by  an  extension  of  the  method 
for  saturated  steam,  and  this  method  applies  with  equal  facility 
to  problems  in  which  the  steam  becomes  moist  during  the  expan- 
sion. The  most  ready  method  of  solution  is  by  aid  of  the  tempera- 
ture-entropy table,  which  may  be  entered  at  the  proper  pressure 
(or  the  corresponding  temperature  of  saturated  steam)  and  the 
proper  superheated  temperature,  it  being  in  practice  sufficient  to 
take  the  line  for  the  nearest  tabular  pressure  and  the  column 


PROPERTIES    OF    SULPHUR   DIOXIDE  117 

showing  the  nearest  degree  of  superheating.  Following  down 
the  column  for  entropy  to  the  final  pressure,  the  properties  for 
the  final  condition  will  be  found;  these  will  be  the  heat  con- 
tents, specific  volume,  and  either  the  temperature  of  superheated 
steam  or  the  quality  x,  depending  on  whether  the  steam  remains 
superheated  during  the  expansion  or  becomes  moist. 

If  the  external  work  of  adiabatic  expansion  of  steam  initially 
superheated  is  desired,  it  can  be  had  by  taking  the  difference  of 
the  intrinsic  energies.  The  heat  equivalent  of  intrinsic  energy 
of  moist  steam  is 

xp  +  q  =  x  (r  —  Apu)  +  q  =  xr  +  q  —  Apxu, 

and  of  this  expression  the  quantity  xr  +  q  may  be  taken  from 
the  temperature- entropy  table,  and  the  quantity  Ap  x  u  can 
be  determined  by  aid  of  the  steam  table.  In  like  manner  the 
heat  contents  of  superheated  steam 


which  is  computed  and  set  down  in  the  temperature-entropy 
table  may  be  made  to  yield  the  heat  equivalent  of  the  intrinsic 
energy  by  subtracting  the  heat  equivalent  of  the  external  work 
of  vaporizing  and  superheating  the  steam 

Ap  (v  -  a), 

where  v  is  the  specific  volume  of  the  superheated  steam.  This 
method  is  subject  to  some  criticism,  especially  when  the  steam 
is  not  highly  superheated,  because  some  heat  will  be  required 
to  do  the  disgregation  work  of  superheating.  Fortunately  the 
greater  part  of  problems  arising  in  engineering  involve  the  heat 
contents,  so  that  this  question  is  avoided. 

Properties  of  Sulphur  Dioxide.  —  One  of  the  most  interesting 
and  important  applications  of  the  theory  of  superheated  vapors 
is  found  in  the  approximate  calculation  of  properties  of  certain 
volatile  liquids  which  are  used  in  refrigerating-machines,  and  for 
which  we  have  not  sufficient  experimental  data  to  construct  tables 
in  the  manner  explained  in  the  chapter  on  saturated  vapors. 


SUPERHEATED    VAPORS 

For  example,  Regnault  made  experiments  on  the  pressures 
of  saturated  sulphur  dioxide  and  ammonia,  but  did  not  de- 
termine the  heat  of  the  liquid  nor  the  total  heat.  He  did, 
however,  determine  some  of  the  properties  of  these  substances 
in  the  gaseous  or  superheated  condition,  from  which  it  is  pos- 
sible to]  construct  the  characteristic  equations  for  the  super- 
heated vapors.  These  equations  can  then  be  used  to  make 
approximate  calculations  of  the  saturated  vapors,  for  such  equa- 
tions are  assumed  to  be  applicable  down  to  the  saturated  con- 
dition. Of  course  such  calculations  are  subject  to  a  considerable 
unknown  error,  since  the  experimental  data  are  barely  sufficient 
to  establish  the  equations  for  the  superheated  vapors. 

The  specific  heat  of  gaseous  sulphur  dioxide  is  given  by 
Regnault*  as  0.15438,  and  the  coefficient  of  dilatation  as 
0.0039028.  The  theoretical  specific  gravity  compared  with  air, 
calculated  from  the  chemical  composition,  is  given  by  Landolt 
and  Bornstein  f  as  2.21295.  Gmelin  J  gives  the  following 
experimental  determinations:  by  Thomson,  2.222;  by  Berzelius, 
2.247.  The  figure  2.23  will  be  assumed  in  this  work,  which 
gives  for  the  specific  volume  at  freezing-point  and  at  atmospheric 
pressure 

^  =      -7733  _  0.347  cubic  metres. 
2.23 


The  corresponding  pressure   and   temperature  are  10,333 
273°  C. 

At  this  stage  it  is  necessary  to  assign  a  probable  form  for  the 
characteristic  equation,  and  for  that  purpose  the  form 

pv  =  BT  -  Cpa       ......   (125) 

proposed  by  Zeuner  has  commonly  been  used,  and  it  is  con- 
venient to  admit  that  it  may  take  the  form 

pv  =  -^  aT  -  Cpa  ......   (126) 

A. 

*  M6moires  de  rinstitut  de  France,  tome  xxi,  xxvi. 
f  Physikalische-chemische  Tdbellen. 
}  Watt's  translation,  p.  280. 


PROPERTIES    OF    SULPHUR   DIOXIDE  119 

The  value  of  the  arbitrary  constant  a  may  be  determined 
from  the  coefficient  of  dilatation  as  follows.  The  coefficient 
of  dilatation  is  the  ratio  of  the  increase  of  volume  at  constant 
pressure,  for  one  degree  increase  of  temperature,  to  the  original 
volume;  so  that  the  preceding  equation  applied  at  o°  C.  and  at 
i°  C.  gives  c 


v0  A   p0vQ 

The  value  of  a  obtained  by  substituting  known  values  in  the 
above  equation  is  0.212.  Now  as  a  appears  in  both  the  first  and 
the  last  terms  of  the  right-hand  side  of  equation  (126),  a  con- 
siderable change  in  a  has  but  little  effect  on  the  computations 
by  aid  of  that  equation.  As  will  appear  later  an  assumption 
of  a  value  0.22  for  a  will  make  equation  (126)  agree  well  with 
certain  experiments  on  the  compressibility  of  sulphur  dioxide, 
and  it  will  consequently  be  chosen.  If  now  we  reverse  the  process 
by  which  a  was  calculated  from  the  coefficient  of  dilatation, 
the  latter  constant  will  appear  to  have  a  computed  value  of 
0.004,  which  is  but  little  different  from  the  experimental  value. 

To  compute  C  we  have 

0.15438  X  426.9  X  0.22  =  14.5, 
and  the  coefficient  of  pa  is 

14.^  X  273  —  10333  X  °-347  o          i 

—  "  -  /0         0°2^  -  ^tL-   =  48  nearly; 

i°333  ' 
so  that  the  equation  becomes 

pv  =  14.5  T  -  48  p°'22   .....   (127) 
Regnault  found  for  the  pressures 

pt  =    697.83  mm.  of  mercury, 
p2  =  1341.58  mm.  of  mercury, 
and  at  7°.  7  C.  the  ratio 

1.02088. 


I2d  SUPERHEATED    VAPORS 

Reducing  the  given  pressures  to  kilograms  on  the  square 
metre,  and  the  temperature  to  the  absolute  scale,  and  applying 
to  equation  (127),  we  obtain  1.016  instead  of  the  experimental 
value  for  the  above  ratio. 

Regnault  gives  for  the  pressure  of  saturated  sulphur  dioxide, 
in  mm.  of  mercury,  the  equation 

log  p  =  a  —  ban  —  c^\ 

a  =  5.6663790; 
log  6   =  0.4792425; 
logo   =  9.1659562  —  10; 
logo:  =  9.9972989  —  10; 
log  /?  =  9.98729002  —  10; 

n  =  t  +  28°  C. 

Applying  equation  (95),  page  76,  to  this  case, 


log  a  =  9.9972989; 
log  /?  =  9.98729002; 
log  4  =  8.6352146; 
log  B  =  7.9945332; 
n  =  /  +  28°  C. 

The  specific  volume  of  saturated  sulphur  dioxide  may  be 
calculated  by  inserting  in  equation  (127)  for  the  superheated 
vapor  the  pressures  calculated  by  aid  of  the  above  equation. 
The  results  at  several  temperatures  are  as  follows: 

/  -  30°  C.  o  +  30°  C. 

5  0.8292  0.2256  0.0825 

Andr^efT  *  gives  for  the  specific  gravity  of  fluid  sulphur  dioxide 
1.4336;  consequently  the  specific  volume  of  the  liquid  is 

a-  =  0.0007. 
*  Ann.  Chem.  Pharm.,  1859. 


PROPERTIES    OF    SULPHUR   DIOXIDE  121 

The  value  of  r,  the  heat  of  vaporization,  may  now  be  calcu- 
lated at  the  given  temperatures  by  equation  (106),  page  89, 


'  - 

in  which  u  =  s  —  <r. 

The  results  are 

t  -  30°  C.  o  +  30°  C. 

r  106.9  97.60  90.54 

Within  the  limits  of  error  of  our  method  of  calculation,  the 
value  of  r  may  be  found  by  the  equation 

r  =  98  —  0.27  t     ......   (128) 

The  specific  heat  of  the  liquid  is  derived  by  the  following 
device.  First  assume  that  the  entropy  of  the  superheated  vapor 
may  be  calculated  by  the  equation 

d4>  =  cp%+(c.-cp)    & 

given  on  page  67  for  perfect  gases.      This  may  be  transformed 


into  K  _ 


But  if  we  introduce  into  the  equation  for  a  perfect  gas 

pv  -  RT, 
the  value  of  R  from  the  equation 

Cp        cv  =  A.K.) 
the  characteristic  equation  may  take  the  form 


•     •     •     •   (129) 


A 


Comparison    of    this    equation    with    equation    (126)    suggests 
replacing  the  term  -   in 

/C 

factor  a,  so  that  it  may  read 


replacing  the  term  -   in  equation   (129)    by  the  arbitrary 

/C 


(130) 


I22  SUPERHEATED    VAPORS 

The  expression  for  the  entropy  of  a  liquid  and  its  vapor  is 
fr  +  *  or  ~   +fcdt 

if  the  vapor  is  dry.     When  differentiated  this  yields 

....  (131) 


If  it  be  assumed  that  equations  (130)  and  (131)  may  both  be 
applied  at  saturation  we  have 

Tdp\  dr        r  . 

1""fl"*+'"~     '  '  '  (I32) 


If  it  be  admitted  further  that  the  differential  coefficient  -f-  can 

dt 

be  computed  by  the  equation  on  page  120,  the  above  equation 
affords  a  means  of  estimating  the  specific  heat  of  the  liquid.  At 
o°  C.,  this  method  gives  for  the  specific  heat 

c  =  0.4. 
In  English  units  we  have  for  superheated  sulphur  dioxide 

pv=  26.4  T  -  184  p»™    .....   (133) 

the  pressures  being  in  pounds  on  the  square  foot,  the  volumes 
in  cubic  feet,  and  the  temperatures  in  Fahrenheit  degrees 
absolute. 

For  pressures  in  pounds  on  the  square  inch  at  temperatures 
on  the  Fahrenheit  scale, 

log  p  =  a  —  ban   —  cp"; 


log  b  =  0.4792425; 
log  c  =  9.1659562  —  10; 
log  a  =  9.9984994  —  10; 
log  ft  =  9.99293890  —  10; 
n  =  *  +  i8°.4F. 


PROPERTIES    OF   AMMONIA  123 

For  the  heat  of  vaporization 

r  =  176  -  0.27  (/  -  32) (134) 

and  for  the  specific  heat  of  the  liquid 

c  =  0.4. 

In  applying  these  equations  to  the  calculation  of  a  table  of 
the  properties  of  saturated  sulphur  dioxide  the  pressures  corre- 
sponding to  the  temperatures  are  calculated  as  usual.  Then 
the  heat  of  the  liquid  is  calculated  by  aid  of  the  constant  specific 
heat.  The  heat  of  vaporization  is  calculated  by  aid  of  equation 
(134).  Next  the  specific  volume  is  calculated  by  inserting  the 
given  temperature  and  the  corresponding  pressure  for  the  sat- 
urated vapor  in  the  characteristic  equation  (133).  Having 
the  specific  volume  of  the  vapor  and  that  of  the  liquid,  the  heat 
equivalent  (Apu)  of  the  external  work  is  readily  found.  Finally, 
the  entropy  of  the  liquid  is  calculated  by  the  equation 

6=c\oge— (135) 

1  0 

If  the  reader  should  object  that  this  method  is  tortuous  and 
full  of  doubtful  approximations  and  assumptions,  he  must  bear 
in  mind  that  any  method  that  can  give  approximations  is  better 
than  none,  and  that  all  the  computations  for  refrigerating- 
machines,  that  use  volatile  fluids,  depend  on  results  so  obtained. 
And  further,  much  of  the  waste  and  disappointment  of  earlier 
refrigerating-machines  could  have  been  avoided  if  tables  as  good 
as  those  computed  by  this  method  were  then  available. 

Properties  of  Ammonia.  —  The  specific  heat  of  gaseous 
ammonia,  determined  by  Regnault,  is  0.50836.  The  theoretical 
specific  gravity  compared  with  air,  calculated  from  the  chemical 
composition,  is  given  by  Landolt  and  Bornstein  as  0.58890. 
Gmelin  gives  the  following  experimental  determinations:  by 
Thomson,  0.5931 ;  by  Biot  and  Arago,  0.5967.  For  this  work 
the  figure  0.597  will  be  assumed,  which  gives 'for  the  specif  c 
volume  at  freezing-point  and  at  atmospheric  pressure 

v   =    '7733   _  T  ,0  cubic  metres. 


124 


SUPERHEATED    VAPORS 


The  coefficient  of  dilatation  has  not  been  determined,  and  con- 
sequently cannot  be  used  to  determine  the  value  of  a  in  equation 
(126).  It,  however,  appears  that  consistent  results  are  obtained 
if  a  is  assumed  to  be  £.  The  coefficient  of  T  then  becomes 

0.50836  X  426.9  X  J  =  54.3, 
and  the  coefficient  of  ft  is 

54.3  X  273  —  10333  X  1.30  _ 

— i  i4^» 

I0333 

so  that  the  equation  becomes 

pv  -  54.3  T  -  142  #* (136) 

The  coefficient  of  dilatation,  calculated  by  the  same  process 
as  was  used  in  determining  a  for  sulphur  dioxide,  is  0.00404, 
which  may  be  compared  with  that  for  sulphur  dioxide. 

Regnault  found  for  the  pressures 

Pi  =    7°3-5°  mm-  °f  mercury, 
p2  =  1435-3  mm-  of  mercury, 

and  at  8°.i  C.  the  ratio 

^=  1.0188, 

Pf>* 

while  equation  (136)  gives  under  the  same  conditions  1.0200. 
For  saturated  ammonia  Regnault  gives  the  equation 

log  p  =  a  —  ban  —  eft"; 

a  =  11.5043330; 
log  b  =  0.8721769; 
log  c  =  9.9777087  —  10; 
log  a  =  9.9996014  —  10; 
log  /?  =  9.9939729  —  10; 

n  =  t  +  22°  C.; 


PROPERTIES    OF    AMMONIA 


125 


by  aid  of  which  the  pressures  in  mm.  of  mercury  may  be  calculated 
for  temperatures  on  the  centigrade  scale.  The  differential 
coefficient  may  be  calculated  by  aid  of  the  equation 


log  A  =  8.1635170  —  10; 
log  B  =  8.4822485  —  10; 
log  a  =  9.9996014  —  10; 
log  ft  =  9.9939729  -  10; 
n  =  /  +  22°  C. 

The    specific    volume    of   saturated    ammonia    calculated    by 
equation  (136)  at  several  temperatures  are 

t          -  30°  C.  o  +  30°  C. 

s          0.9982  0.2961  0.1167 

Andreeff  gives  for  the  specific  gravity  of  liquid  ammonia  at 
o°  C.  0.6364,  so  that  the  specific  volume  of  the  liquid  is 

cr  =  0.0016. 

The  values  of  r  at  the  several  given  temperatures,  calculated 
by  equation  (128),  are 

t  -3o°C.  o  +3o°C. 

r  325-7  S00'^  277-5 

which  may  be  represented  by  the  equation 
r  =  300  —  0.8  /. 

The  specific  heat  of  the  liquid,  calculated  by  aid  of  equation 

(132),  is 

c  =  i.i. 

In   English  units  the  properties   of  superheated   or  gaseous 
ammonia  may  be  represented  by  the  equation 

pv  =  99  T--  710  #*, 

in  which  the  pressures  are  taken  in  pounds  on  the  square  foot 
and  volumes  in  cubic  feet,  while  T  represents  the  absolute 
temperature  in  Fahrenheit  degrees. 


I26  SUPERHEATED    VAPORS 

The  pressure  in  pounds  on  the  square  inch  may  be  calculated 
by   the   equation 

log  p  =  a  —  ban  —  cjP\ 

a  =  9.7907380; 
log  b  =  0.8721769  —  10; 
log  c  =  9.9777087  —  10; 
log  a  =  9.9997786  —  10; 
log  ft  =  9.9966516  —  10; 
n  =  t  +  7°.6  F. 

The  heat  of  vaporization  may  be  calculated  by  the  equation 

r  =  540  -  0.8  (/  —  32), 
and  the  specific  heat  of  the  liquid  is 

c  =  i.i. 

EXAMPLES. 

1.  What  is  the  weight  of  one  cubic  foot  of  superheated  steam 
at  500°  F.  and  at  60  pounds  pressure  absolute  ?     Knoblauch's 
equation.       Ans.  0.106  pounds. 

2.  At  129.3  pounds  gauge  pressure  2  pounds  of  steam  occupy 
7  cubic  feet.    Find  its  temperature.    Assume  value  of   T  for 
entering  Table  i,  page  112,  and  solve  by  trial.     Ans.  424°  F. 

3.  What  is  the  volume  of  5  pounds  of  steam  at  129.3  pounds 
gauge  pressure  and  at  3 59°. 5  F:?    Ans.  15.8. 

4.  Superheated  steam  at  50  pounds  absolute  has  three-fourths 
the  density  of  saturated  steam  at  the  same  pressure.     What  is  the 
temperature  ?    Ans.  482°  F. 

5.  A  cubic  foot  of  steam  at  140  pounds  absolute  weighs  0.30 
pounds.     What  is  its  temperature?     Ans.  374°  F. 

6.  Two  pounds  of  steam  and  water  at  129.3  pounds  pressure 
above  the  atmosphere  occupy  6  cubic  feet.     Heat  is  added  and 
the  pressure  kept  constant  till  the  volume  is  8.5  cubic  feet.     Find 
the  final  condition,  and  the  external  work  done  in  expanding. 
Ans.  Temperature  68i°F.;  work  51800. 


EXAMPLES 


127 


7.  Saturated  steam  at  150  pounds  gauge,  containing  2  per  cent 
of  water,  passes  through  a  superheater  on  its  way  to  an  engine. 
Its  final  temperature  is  400°  F.     Find  the  increase  in  volume 
and  the  heat  added  per  pound.      Ans.  0.222  cubic  feet;  39  B.T.U. 

8.  Let  the  initial  temperature  of  superheated  steam  be  380°  F. 
at  the  pressure  of  150  pounds  absolute.     Find  the  condition 
after  an  adiabatic  expansion  to  20  pounds  absolute.     Determine 
also  the  initial  and  final  volumes.     Ans.    (i)  0.895;   (2)  3.09 
cubic  feet;   (3)  17.8  cubic  feet. 

9.  In  example  14,  page  109,  suppose  that  the  steam  at  cut-off 
were   superheated   10°  F.   above  the  temperature   of  saturated 
steam   at   the   given   pressure,    and   solve   the   example.     Ans. 
(i)  0.887;  (2)  87°  superheating;  (3)  same  as  before;  (4)  n~ 
I-I37J  (5)  *972  and  1950  foot-pounds. 


CHAPTER  VIII. 

THE   STEAM-ENGINE. 

THE  steam-engine  is  still  the  most  important  heat-engine, 
though  its  supremacy  is  threatened  on  one  hand  by  the  steam- 
turbine  and  on  the  other  by  the  gas-engine.  When  of  large  size 
and  properly  designed  and  managed  its  economy  is  excellent  and 
can  be  excelled  only  by  the  largest  and  best  gas-engines, 
and  in  many  cases  these  engines  (even  with  the  advantage  of 
a  more  favorable  range  of  temperature)  depend  for  their  com- 
mercial success  on  the  utilization  of  by-products. 

It  can  be  controlled,  regulated,  and  reversed  easily  and  posi- 
tively —  properties  which  are  not  possessed  in  like  degree  by 
other  heat-engines.  It  is  interesting  to  know  that  the  theory 
of  thermodynamics  was  developed  mainly  to  account  for  the 
action  and  to  provide  methods  of  designing  steam-engines; 
though  neither  object  is  entirely  accomplished,  on  account  of 
the  fact  that  the  engine-cylinder  must  be  made  of  some  metal  to 
be  hard  and  strong  enough  to  endure  service,  for  all  metals  are 
good  conductors  of  heat,  and  seriously  affect  the  action  of  a  con- 
densable fluid  like  steam. 

Carnot's  Cycle  for  a  steam-engine  is  repre- 
sented by  Fig.  31,  in  which  ab  and  cd  are 
]^    isothermal  lines,  representing  the  application 
and  rejection  of  heat  at  constant  temperature 
and    at    constant  pressure,     be  and  da  are 
:   adiabatic  lines,  representing  change  of  tem- 
perature and  pressure,  without  transmission 
of   heat   through  the  walls  of  the  cylinder. 
The  diagram  representing  Carnot  's  cycle  has  an  external  resem- 
blance   to    the    indicator-diagram   from   some   actual   engines, 
but  it  differs  in  essential  particulars. 

128 


CARNOT'S    CYCLE 


129 


In  the  condition  represented  by  the  point  a  the  cylinder  con- 
tains a  mixture  of  water  and  steam  at  the  temperature  tl  and 
the  pressure  pt.  If  connection  is  made  with  a  source  of  heat 
at  the  temperature  tlt  and  heat  is  added,  some  of  the  water  will 
be  vaporized  and  the  volume  will  increase  at  constant  pressure 
as  represented  by  ab.  If  thermal  communication  is  now  inter- 
rupted, adiabatic  expansion  may  take  place  as  represented  by  be 
till  the  temperature  is  reduced  to  /2,  the  temperature  of  the 
refrigerator,  with  which  thermal  communication  may  now  be 
established.  If  the  piston  is  forced  toward  the  closed  end  of 
the  cylinder  some  of  the  steam  in  it  will  be  condensed,  and  the 
volume  will  be  reduced  at  constant  pressure  as  represented  by 
cd.  The  cycle  is  completed  by  an  adiabatic  compression  rep- 
resented by  da. 

If  the  absolute  temperature  of  the  source  of  heat  is  7\,  and 
if  that  of  the  refrigerator  is  T2,  then  the  efficiency  is 


whatever  may  be  the  working  fluid. 

For  example,  if  the  pressure  of  the  steam  during  isothermal 
expansion  is  100  pounds  above  the  atmosphere,  and  if  the  pressure 
during  isothermal  compression  is  equal  to  that  of  the  atmos- 
phere, then  the  temperatures  of  the  source  of  heat  and  of  the 
refrigerator  are  337°.6  F.  and  212°  F.,  or  797.1  and  671.5  abso- 
lute, so  that  the  efficiency  is 

707.1  —  671.=; 

121—      —^—^=0.157. 


797.1 


The  following  table  gives  the  efficiencies  worked  out  in  a 
similar  way,  for  various  steam-  pressures,  —  both  for  /2  equal  to 
21  2°  F.,  corresponding  to  atmospheric  pressure,  -and  for  /2, 
equal  to  n6°F.,  corresponding  to  an  absolute  pressure  of  1.5 
pounds  to  the  square  inch: 


THE   STEAM-ENGINE 


EFFICIENCY  OF  CARNOT'S  CYCLE   FOR   STEAM-ENGINES. 


Initial  Pressure 

by  the  Gauge, 
above  the 

Atmospheric 
Pressure. 

1.5  Pounds 
Absolute. 

Atmosphere. 

15 
3° 

0-053 
0.084 

0.189 
0.215 

60 

o.  124 

0.249 

100 

0.1157 

0.278 

15° 

0.186 

0.302 

200 

0.207 

0.320 

300 

o.  238 

°-347 

The  column  for  atmospheric  pressure  may  be  used  as  a 
standard  of  comparison  for  non-condensing  engines,  and  the 
column  for  1.5  pounds  absolute  may  be  used  for  condensing 
engines. 

It  is  interesting  to  consider  the  condition  of  the  fluid  in  the 
cylinder  at  the  different  points  of  the  diagram  for  Carnot's 
cycle.  Thus  if  the  fluid  at  the  condition  represented  by  b  in 
Fig.  31  is  made  up  of  xb  part  steam  and  i  —  xb  part  water,  then 
from  equation  (118)  the  condition  at  the  point  c  is  given  by 


In  like  manner  the  condition  of  the  mixture  at  the  point  d  is 

*,!=  W-*.  +  *I-<0     ....    (I38) 


It  is  interesting  to  note  that  if  xb  is  larger  than  one-half,  that 
is,  if  there  is  more  steam  than  water  in  the  cylinder  at  b,  then 
the  adiabatic  expansion  is  accompanied  by  condensation.  Again, 
if  xa  is  less  than  one-half,  then  the  adiabatic  compression  is  also 
accompanied  by  condensation.  Very  commonly  it  is  assumed 
that  xb  is  unity,  so  that  there  is  dry  saturated  steam  in  the  cylin- 
der at  6;  and  that  xa  is  zero,  so  that  there  is  water  only  in  the 


0.1    0.2     0.3     0.4     0.5     0.6     0.7     0.8     0..9 


EFFICIENCY   OF   CARNOT'S   CYCLE  131 

cylinder  at  a;  but  there  is  no  necessity  for  such  assumptions, 
and  they  in  no  way  affect  the  efficiency. 

The  temperature-entropy  diagram  for  Carnot's  cycle  for  a 
steam-engine  is  shown  by  Fig.  32,  on  which  are  drawn  also  the 
lines  for  entropy  of  the  liquid 
ma,  and  the  entropy  of  satur- 
ated vapor  be,  as  well  as  the 
lines  which  represent  the  value 
of  x,  the  dryness  factor.  This 
diagram  represents  to  the  eye 
the  vaporization  during  the 
isothermal  expansion  ab,  the 
partial  condensation  during 
the  adiabatic  expansion  be,  FIG.  33. 

the  isothermal  condensation  along  cd,  and  the  condensation 
during  the  adiabatic  compression  da.  In  the  diagram  the  work- 
ing substance  is  shown  as  water  at  a  and  as  dry  steam  at  b\ 
the  efficiency  would  clearly  be  the  same  for  a  cycle  a'  b'  c*  dfy 
which  contains  a  varying  mixture  of  water  and  steam  under  all 
conditions. 

If  the  cylinder  contains  M  pounds  of  steam  and  water,  the 
heat  absorbed  by  the  working  substance  during  isothermal 
expansion  is 

Ql  =  Mrt  (xb  -  xa) (139) 

and  the  heat  rejected  during  isothermal  compression  is 
Q2  =  Mr2  (xc  -  X0), 

so  that  the  heat  changed  into  work  during  the  cycle  is 
Q1  -  Q2  =  M\r^   (xb  -  xa)  -  r2  (XG  -  xd)\ 

But  from  equations   (137)  and  (138) 


2  (x0  -  xd)  =  --^rl  (xb  -  xa), 


132  THE    STEAM-ENGINE 

and  the  expression  for  the  heat  changed  into  work  becomes 

Ql  -  Q2  =  Mr,  (xb  -  xa)  TI  ~  T?'  .     .     .   (140) 

1 1 

This  equation  is  deduced  because  it  is  convenient  for  making 
comparisons  of  various  other  volatile  liquids  and  their  vapors, 
with  steam,  for  use  in  heat-engines.  It  is  of  course  apparent 

that  Q,  -Q.      T,  -T, 

Qi  Ti 

from  equations  (139)  and  (140),  a  conclusion  which  is  known 
independently,  and  indeed  is  necessary  in  the  development  of 
the  theory  of  the  adiabatic  expansion  of  steam. 

In  the  discussion  thus  far  it  has  been  assumed  that  the  work- 
ing fluid  is  steam,  or  a  mixture  of  steam  and  water.  But  a 
mixture  of  any  volatile  liquid  and  its  vapor  will  give  similar 
results,  and  the  equations  deduced  can  be  applied  directly.  The 
principal  difference  will  be  due  to  the  properties  of  the  vapor 
considered,  especially  its  specific  pressures  and  specific  volumes 
for  the  temperatures  of  the  source  of  heat  and  the  refrigerator. 

For  example,  the  efficiency  of  Carnot's  cycle  for  a  fluid 
working  between  the  temperatures  160°  C.  and  40°  C.  is 

1 60  —  40 

— -*—  =  0.277. 

i 60  +  273 

The  properties  of  steam  and  of  chloroform  at  these  tempera- 
tures are  Steam.  Chloroform. 

40°  C.  160°  C.  40°  C.  160°  C. 

Pressure,  mm.  mercury     .    .      55.13             4^33-  369.26  8734.2 

Volume,  cubic  meters    ...      19.57                   0-3063  0.4449  0.0243 

Heat  of  vaporization,  r     .    .   574.2  496-5  63-I3  5°-53 

Entropy  of  liquid,  6  .    .    .    .        0.1368               0.4644  0.03196  0.11041 

For  simplicity,  we  may  assume  that  one  kilogram  of  the  fluid 
is  used  in  the  cylinder  for  Carnot's  cycle,  and  that  xb  is  unity 
while  xa  is  zero,  so  that  from  equation  (140) 

T   —  T 

r\  r\ ,.,    -*•  i          J  2  . 


EFFICIENCY   OF   CARNOT'S    CYCLE  133 

and  for  steam 

Ql  -  <22  =  496.5  X  0.277  =  137  calories, 
while  for  chloroform 

Qi  -  ft  =  5°-53  X  °-277  =  i4  calories. 

After  adiabatic  expansion  the  qualities  of  the  fluid  will  be,  from 
equation  (137),  for  steam 

_  40^273  (496.5      +       6      _  a     6g\  =  ag 
574.2     Vi6o  +  273  / 

and  for  chloroform 

40  +  273  /     50.53  ,\ 

xc  =  ^—. "*     , h  0.11041  —  0.03 196  1  =  0.969. 

63.13     \i6o  +  273  / 

The  specific  volumes  after  adiabatic  expansion  are,  conse- 
quently, for  steam 

vc  =  xcu2  +  a  =  0.804  (19.57  ~~  o.ooi)  +  o.ooi  =  16.4, 
and  for  chloroform 
vc  =  xcu2  +  a-  =  0.969  (0.4449  -  0.000655)  +  0.000655  =  0.431. 

These  values  for  vc  just  calculated  are  the  volumes  in  the 
cylinder  at  the  extreme  displacement  of  the  piston,  on  the 
assumption  that  one  kilogram  of  the  working  fluid  is  vaporized 
during  isothermal  expansion.  A  better  idea  of  the  relative 
advantages  of  the  two  fluids  will  be  obtained  by  finding  the 
heat  changed  into  work  for  each  cubic  metre  of  maximum  piston- 
displacement,  or  for  a  cylinder  having  the  volume  of  one  cubic 
metre.  This  is  obtained  by  dividing  Q1  —  Q2,  the  heat  changed 
into  work  for  each  kilogram  by  ve.  For  steam  the  result  is 

(Qi  -  Q,)  -  vc  =  137  *  16.4  =  8.3, 

and  for  chloroform  it  is 

(Qi  ~  Q3)  -*-  v.  -  14  +  0.431  =  34; 

from  which  it  appears  that  for  the  same  volume  chloroform 
can  produce  more  than  three  and  a  half  times  as  much  power. 


134  THE    STEAM-ENGINE 

Even  if  we  consider  that  the  difference  of  pressure  for  chloro- 
form, 

.2  -  369-3  =  8364.9  mm., 


is  nearly  twice  that  for  steam,  which  has  only 
4633  -  55  =  4578  mm. 

difference  of  pressure,  the  advantage  appears  to  be  in  favor  of 
chloroform.  If,  however,  the  difference  of  pressures  given  for 
chloroform  is  allowable  also  for  steam,  giving 

8364.9  +  55.1  =  8420  mm. 

for  the  superior  pressure,  then  the  initial  temperature  for  steam 
becomes  185°  C.,  and  the  efficiency  becomes 

185  -40 

- 


instead  of  0.277.  On  the  whole,  steam  is  the  more  desirable 
fluid,  even  if  we  do  not  consider  the  inflammable  and  poisonous 
nature  of  chloroform.  Similar  calculations  will  show  that  on 
the  whole  steam  is  at  least  as  well  adapted  for  use  in  heat-engines 
as  any  other  saturated  fluid;  in  practice,  the  cheapness  and 
incombustibility  of  steam  indicate  that  it  is  the  preferable  fluid 
for  such  uses. 

Non-conducting  Engine.  Rankine  Cycle.  —  The  conditions 
required  for  alternate  isothermal  expansion  and  adiabatic  expan- 
sion cannot  be  fulfilled  for  Carnot's  cycle  with  steam  any  more 
than  they  could  be  for  air.  The  diagram  for  the  cycle  with 
steam,  however,  is  well  adapted  to  production  of  power;  the 
contrary  is  the  case  with  air,  as  has  already  been  shown. 

In  practice  steam  from  a  boiler  is  admitted  to  the  cylinder  of 
the  steam-engine  during  that  part  of  the  cycle  which  corre- 
sponds to  the  isothermal  expansion  of  Carnot's  cycle,  thus  trans- 
ferring the  isothermal  expansion  to  the  boiler,  where  steam  is 
formed  under  constant  pressure.  In  like  manner  the  isothermal 
compression  is  replaced  by  an  exhaust  at  constant  pressure, 
during  which  steam  may  be  condensed  in  a  separate  condenser, 


NON-CONDUCTING   ENGINE  135 

cooled  by  cold  water.  The  cylinder  is  commonly  made  of  cast 
iron,  and  is  always  some  kind  of  metal;  there  is  consequently 
considerable  interference  due  to  the  conductivity  of  the  walls  of 
the  cylinder,  and  the  expansion  and  compression  are  never 
adiabatic.  There  is  an  advantage,  however,  in  discussing  first 
an  engine  with  a  cylinder  made  of  some  non-conducting  material, 
although  no  such  material  proper  for  making  cylinders  is  now 
known. 

The  diagram  representing  the  operations  in  a  non-conducting 
cylinder  for  a  steam-engine  (sometimes  called  the  Rankine  cycle) 
can  be  represented  by  Fig.  33.  ab  represents 
the  admission  of  dry  saturated  steam  from 
the  boiler;  be  is  an  adiabatic  expansion  to  the 
exhaust  pressure;  cd  represents  the  exhaust; 


and   da  is  an  adiabatic   compression   to  the  FlGt  33. 

initial  pressure.  It  is  assumed  that  the  small 
volume,  represented  by  a,  between  the  piston  and  the  head  of 
the  cylinder  is  filled  with  dry  steam,  and  that  the  steam  remains 
homogeneous  during  exhaust  so  that  the  quality  is  the  same  at 
d  as  at  c.  These  conditions  are  consistent  and  necessary, 
since  the  change  of  condition  due  to  adiabatic  expansion  (or 
compression)  depends  only  on  the  initial  condition  and  the 
initial  and  final  pressures;  so  that  an  adiabatic  expansion  from 
a  to  d  would  give  the  same  quality  at  d  as  that  found  at  c  after 
adiabatic  expansion  from  6,  and  conversely  adiabatic  compres- 
sion from  d  to  a  gives  dry  steam  at  a  as  required. 

The  cycle  represented  by  Fig.  33  differs  most  notably  from 
Carnot's  cycle  (Fig.  32)  in  that  ab  represents  admission  of  steam 
and  cd  represents  exhaust  of  steam,  as  has  already  been  pointed 
out.  It  also  differs  in  that  the  compression  da  gives  dry  steam 
instead  of  wet  steam.  The  compression  line  da  is  therefore 
steeper  than  for  Carnot's  cycle,  and  the  area  of  the  figure  is 
slightly  larger  on  this  account.  This  curious  fact  does  not 
indicate  that  the  cycle  has  a  higher  efficiency;  on  the  contrary, 
the  efficiency  is  less,  and  the  cycle  is  irreversible. 

If  the  pressure  during   admission   (equal  to   the  pressure  in 


THE    STEAM-ENGINE 


the  boiler)  is  pv  and  if  the  pressure  during  exhaust  is  pv  then 
the  heat  required  to  raise  the  water  resulting  from  the  conden- 
sation of  the  exhaust-steam  is 


where  q1  is  the  heat  of  the  liquid  at  the  pressure  pv  and  q2  is  the 
heat  of  the  liquid  at  the  pressure  p2.  The  heat  of  vaporization 
at  the  pressure  p1  is  rv  so  that  the  heat  required  to  raise  the  feed- 
water  from  the  temperature  of  the  exhaust  to  the  temperature 
in  the  boiler  and  evaporate  it  into  dry  steam  is 

61  =  'i  +?i  -  03     ......   (X4i) 

and  this  is  the  quantity  of  heat  supplied  to  the  cylinder  per 
pound  of  steam. 

The  steam  exhausted  from  the  cylinder  has  the  quality  x2, 
calculated  by  aid  of  the  equation 


and  the  heat  that  must  be  withdrawn  when  it  is  condensed  is 

62  =  */2     .....     •     •   042) 

this  is  the  heat  rejected  from  the  engine.     The  heat  changed 
into  work  per  pound  of  steam  is 

Ql    ~    <?2    =    ri    +   01    ~    03    ~    X2r2      ....     (143) 

The  efficiency  of  the  cycle  is 


+     - 


(I44) 


If  values  are  assigned  to  pl  and  p2  and  the  proper  numerical 
calculations  are  made,  it  will  appear  that  the  efficiency  for  a 
non-conducting  engine  is  always  less  than  the  efficiency  for 
Carnot's  cycle  between  the  corresponding  temperatures. 

It  should  be  remarked  that  the  efficiency  is  not  affected  by 
the  clearance  or  space  between  the  piston  and  the  head  of  the 
cylinder  and  the  space  in  the  steam-passages  of  the  cylinder, 
provided  that  the  clearance  is  filled  with  dry  saturated  steam  as 


USE   OF   THE   TEMPERATURE-ENTROPY    DIAGRAM 


137 


indicated  in  Fig.  33.  This  is  evident  from  the  fact  that  no  term 
representing  the  clearance,  or  volume  at  a,  Fig.  33,  appears  in 
equation  (144).  Or,  again,  we  may  consider  that  the  steam  in 
the  cylinder  at  the  beginning  of  the  stroke,  occupying  the  vol- 
ume represented  by  a,  expands  during  the  adiabatic  expansion 
and  is  compressed  again  during  compression,  so  that  one 
operation  is  equivalent  to  and  counterbalances  the  other,  and 
so  does  not  affect  the  efficiency  of  the  cycle. 

Use  of  the  Temperature-Entropy  Diagram.  —  The  Rankine 
cycle  is  drawn  with  a  varying  quantity  of  steam  in  the  cylinder, 
beginning  at  a,  Fig.  33,  with  the  steam  caught  in  the  clearance 
and  finishing  at  b,  with  that  weight  plus  the  weight  drawn  from 
the  boiler;  consequently  a  proper  temperature- entropy  diagram, 
which  represents  the  changes  of  one  pound  of  the  working  sub- 
stance, cannot  be  drawn. 

We  may,  however,  use  the  temperature- entropy  diagram 
(like  Fig.  30,  page  104,  or  the  plate  at  the  end  of  the  book)  for 
solving  problems  connected  with  that  cycle  instead  of  equations 
(143)  and  (144). 

In  the  first  place  we  have  by  equa- 
tion (96),  page  83, 

q  =••  J  cdt, 
and  by  equation  (113),  page  97, 

e-  f- 

J    T 

for  a  volatile  liquid.     From  the  latter 
we  have 

cdt  =  TdB; 
therefore 

TdB. 


(760 


160 


FIG.  34- 


From  this  last  equation  it  is  evident  that  the  heat  of  the  liquid  q\ 
for  water  represented  by  the  point  a  in  Fig.  34,  is  measured  by 


138  THE    STEAM-ENGINE 

the  area  Omao.  In  like  manner  the  heat  of  the  liquid  q2  cor- 
responding to  the  point  d,  is  represented  by  the  area  Omdn* 
Again,  the  heat  added  during  the  vaporization  represented  by 

ab,  is  rv  while  the  increase  of  entropy  is  —  J-  .    Therefore  the  heat 

•*  i 
of  vaporization  can  be  represented  by  the  area  oabp.     In  like 

manner  the  partial  vaporization  x2r2  can  be  represented  by  the 
area  ndcp.  Therefore  the  heat  changed  into  work  for  the  cycle 
in  Fig.  33,  which  has  been  represented  by 


can  equally  well  be  represented  by  the  area 

abed  =   area  Omao  +  area  oabp 
—  (area  Omdn  -f-  area  ndcp). 

It  will  consequently  be  sufficient  to  measure  the  area  abed 
by  any  means,  for  example,  by  aid  of  a  planimeter,  in  order  to 
determine  the  heat  changed  into  work  during  the  operation  of  the 
non-conducting  engine  working  on  the  Rankine  cycle.  If  the  plan- 
imeter determines  the  area  in  square  inches,  the  scale  of  the  draw- 
ing for  Fig.  34  should  be  one  inch  per  degree,  and  one  inch  per 
unit  of  entropy,  or,  if  other  and  more  convenient  scales  are  to  be 
used,  proper  reductions  must  be  made  to  allow  for  those  scales. 

It  must  be  firmly  fixed  in  mind  that  the  use  of  a  diagram  like 
Fig.  34  is  justified  because  it  has  been  proved  that  the  area 
abed  (drawn  to  the  proper  scale)  is  numerically  equal  to  the 
heat  changed  into  work  as  computed  by  equation  (143),  and 
that  the  diagram  does  not  represent  the  operations  of  the  cycle. 
This  is  entirely  different  from  the  case  of  the  diagram,  Fig.  32, 
which  correctly  represents  the  operations  of  Carnot's  cycle. 

The  illustration  of  the  use  of  the  temperature-entropy  diagram 
for  this  purpose  is  chosen  for  convenience  with  dry  saturated 
steam  at  b,  Fig.  34.  It  is  evident  that  it  could  (with  equal 
propriety)  be  applied  to  an  engine  supplied  with  moist  steam  if 
rl  is  replaced  by  xlr1  in  equation  (143)  and  if  b  is  located  at  the 
proper  place  between  a  and  b. 

The  actual  measurement  of  areas  by  a  planimeter  is  seldom 


INCOMPLETE    CYCLE  139 

if  ever  applied,  but  the  diagram  is  used  effectively  in  the  dis- 
cussion of  certain  problems  of  non-reversible  flow  of  steam  in 
nozzles  and  turbines,  with  allowance  for  friction. 

It  further  suggests  an  approximation  that  may  sometimes  be 
useful,  especially  if  the  change  of  pressure  (and  temperature)  is 
small.  Thus  the  area  abed  may  be  approximately  represented 
by  the  expression 

i.  (ab  +  dc)  be  =  l~(^- 
so  that  in  place  of  equation  (143)  we  may  have 

i  ~  g  •  •  •  •  (I4S) 


for  the  heat  changed  into  work  by  Rankine's  cycle. 

This  approximation  depends  on  treating  ad  as  a  straight  line, 
and  this  assumption  is  more  correct  as  the  difference  of  temper- 
ature is  less;  that  is  for  those  cases  in  which  equation  (143) 
deals  with  the  difference  of  quantities  of  about  the  same  magni- 
tude, and  may  consequently  be  affected  by  a  large  relative  error. 

Temperature-Entropy  Table.  —  The  temperature-entropy  table 
which  has  been  described  on  page  106  was  computed  for  solu- 
tion of  problems  of  this  nature,  more  especially  in  turbine 
design,  and  enables  us  to  determine  the  heat  changed  into  work 
directly  with  sufficient  accuracy  for  engineering  work,  without 
interpolation  ;  it  also  gives  the  quality  x  and  the  specific  volume. 

Incomplete  Cycle.  —  The  cycle  for  a  non-conducting  engine 
may  be  incomplete  because  the  expansion  is  not  carried  far 
enough  to  reduce  the  pressure  to  that 
of  the  back-pressure  line,  as  is  shown 
in  Fig.  35.  Such  an  incomplete  cycle 
has  less  efficiency  than  a  complete  cycle, 
but  in  practice  the  advantage  of  using 
a  smaller  cylinder  and  of  reducing  fric- 
tion is  sufficient  compensation  for  the 

small   loss   of  efficiency  due  to  a  moderate  drop  at  the  end  of 
the  stroke,  as  shown  in  Fig.  35. 


THE    STEAM-ENGINE 

The  discussion  of  the  incomplete  cycle  is  simplified  by  assum- 
ing that  there  is  no  clearance  and  no  compression  as  is  indicated 
by  Fig.  35.  It  will  be  shown  later  that  the  efficiency  will  be  the 
same  with  a  clearance,  provided  the  compression  is  complete. 

The  most  ready  way  of  finding  the  efficiency  for  this  cycle  is 
to  determine  the  work  of  the  cycle.  Thus  the  work  during 
admission  is 

Pi  (ui  +  °")> 

where  u±  is  the  increase  of  volume  due  to  vaporization  of  a  pound 
of  steam,  and  <r  is  the  specific  volume  of  water.  The  work  during 
expansion  is 

Eb  -  Ec  =  j  ^  +  ft  -  xcpc  -  qc), 

where  ql  and  pl  are  the  heat  of  the  liquid  and  the  heat-equivalent 
of  the  internal  work  during  vaporization  at  the  pressure  pv 
while  qc  and  pc  are  corresponding  quantities  for  the  pressure  at  c. 
xc  is  to  be  calculated  by  the  equation 

xc  =  - 

The  work  done  by  the  piston  on  the  steam  during  exhaust  is 
p2  (xcuc  +  a-). 

The  total  work  of  the  cycle  is  obtained  by  adding  the  work 
during  admission  and  expansion  and  subtracting  the  work 
during  exhaust,  giving 

The  last  term  is  small,  and  may  be  neglected.  Adding  and 
subtracting  Apcxcuc  and  multiplying  by  A,  we  get  for  the  heat- 
equivalent  of  the  work  of  the  cycle 

Qi  -  <22  =  ri  -  xc'rc  +  A  (pc  -  p2)  ucxc  +  q1  -  qe   (14?)     \ 


STEAM-CONSUMPTION   OF   NON-CONDUCTING   ENGINE      141 

which  is  equal  to  the  difference  between  the  heat  supplied  and 
the  heat  rejected  as  indicated.  The  heat  supplied  is 

Qi  =  ri  +  0i  -  ?2> 

as  was  deduced  for  the  complete  cycle;  the  cost  of  making  the 
steam  remains  the  same,  whether  or  not  it  is  used  efficiently. 
Finally,  the  efficiency  of  the  cycle  is 

~  Qi        '1  +  ?i  -  XJ*  ~  <!c  +  A  (pc  -  pj  xcuc 


e  = 


+    0       - 


xcu 


If  ^>c  is  made  equal  to  pz  in  the  preceding  equation,  it  will  be 
reduced  to  the  same  form  as  equation  (144),  because  the  expan- 
sion in  such  case  becomes  complete. 

Steam-Consumption  of  Non-conducting  Engine.  —  A  horse- 
power is  33000  foot-pounds  per  minute  or  60  X  33000  foot-pounds 
per  hour.  But  the  heat  changed  into  work  per  pound  of  steam 
by  a  non-conducting  engine  with  complete  expansion  is,  by 
equation  (143), 


so  that  the  steam  required  per  horse-power  per  hour  is 

_  60  X  33000  _ 
778  (rl  +  q,  -  q2  -  */2) 

Similarly,  the  steam  per  horse-power  per  hour  for  an  engine 
with  incomplete  expansion,  by  aid  of  expression  (146),  is 

60  X  33000 
778  (p,  +  Ap^  -  xcpe  -  Ap'2xcuc  +qt-  qc)  ' 

The  value  of  x2  or  xc  is  to  be  calculated  by  the  general  equation 


The  denominator  in  either  of  the  above  expressions  for  the 
steam  per  horse-power  per  hour  is  of  course  the  work  done  per 
pound  of  steam,  and  the  parenthesis  without  the  mechanical 


142  THE    STEAM-ENGINE 

equivalent  778  is  equal  to  Ql  —  Qr  If  then  we  multiply  and 
divide  by 

61  -  'i  +  fc  -  v» 

that  is,  by  the  heat  brought  from  the  boiler  by  one  pound  of 
steam,  we  shall  have  in  either  case  for  the  steam  consumption 
in  pounds  per  hour 

60  X  33000  X  Qt  _          60  X  33000  ,       s 

778  (Q,  -  Q,)  Q,  ~ 


where 

-V1 

is  the  efficiency  for  the  cycle. 

Actual  Steam-Engine.  —  The  indicator-diagram  from  an  actual 
steam-engine  differs  from  the  cycle  for  a  non-conducting  engine 
in  two  ways:  there  are  losses  of  pressure  between  the  boiler  and 
the  cylinder  and  between  the  cylinder  and  the  condenser,  due 
to  the  resistance  to  the  flow  of  steam  through  pipes,  valves,  and 
passages;  and  there  is  considerable  interference  of  the  metal  of 
the  cylinder  with  the  action  of  the  steam  in  the  cylinder.  The 
losses  of  pressure  may  be  minimized  for  a  slow-moving  engine 
by  making  the  valves  and  passages  direct  and  large.  The 
interference  of  the  walls  of  the  cylinder  cannot  be  prevented, 
but  may  be  ameliorated  by  using  superheated  steam  or  by  steam- 
jacketing. 

When  steam  enters  the  cylinder  of  an  engine,  some  of  it  is 
condensed  on  the  walls  which  were  cooled  by  contact  with 
exhaust-steam,  thereby  heating  them  up  nearly  to  the  tempera- 
ture of  the  steam.  After  cut-off  the  pressure  of  the  steam  is 
reduced  by  expansion  and  some  of  the  water  on  the  walls  of 
the  cylinder  vaporizes.  At  release  the  pressure  falls  rapidly 
to  the  back-pressure,  and  the  water  remaining  on  the  walls  is 
nearly  if  not  all  vaporized.  It  is  at  once  evident  that  so  much 
of  the  heat  as  remains  in  the  walls  until  release  and  is  thrown 
out  during  exhaust  is  a  direct  loss;  and  again,  the  heat  which 
is  restored  during  expansion  does  work  with  less  efficiency, 


ACTUAL   STEAM-ENGINE  143 

because  it  is  reevaporated  at  less  than  the  temperature  in  the 
boiler  or  in  the  cylinder  during  admission.  A  complete  state- 
ment of  the  action  of  the  walls  of  the  cylinder  of  an  engine, 
with  quantitative  results  from  tests  on  engines,  was  first  given 
by  Hirn.  His  analysis  of  engine  tests,  showing  the  interchanges 
of  heat  between  the  walls  of  the  cylinder  and  the  steam,  will  be 
given  later.  It  is  sufficient  to  know  now  that  a  failure  to  con- 
sider the  action  of  the  walls  of  the  cylinder  leads  to  gross  errors, 
and  that  an  attempt  to  base  the  design  of  an  engine  on  the  theory 
of  a  steam-engine  with  a  non-conducting  cylinder  can  lead  only 
to  confusion  and  disappointment. 

The  most  apparent  effect  of  the  influence  of  the  walls  of  the 
cylinder  on  the  indicator-diagram  is  to  change  the  expansion 
and  the  compression  lines ;  the  former  exhibits  this  change  most 
clearly.  In  the  first  place  the  fluid  in  the  cylinder  at  cut-off 
consists  of  from  twenty  to  fifty  per  cent  hot  water,  which  is  found 
mainly  adhering  to  the  walls  of  the  cylinder.  Even  if  there 
were  no  action  of  the  walls  during  expansion  the  curve  would  be 
much  less  steep  than  the  adiabatic  line  for  dry  saturated  steam. 
But  the  reevaporation  during  expansion  still  further  changes  the 
curve,  so  that  it  is  usually  less  steep  than  the  rectangular 
hyperbola. 

It  may  be  mentioned  that  the  fluctuations  of  temperature 
in  the  walls  of  a  steam-engine  cylinder  caused  by  the  conden- 
sation and  reevaporation  of  water  do  not  extend  far  from  the  sur- 
face, but  that  at  a  very  moderate  depth  the  temperature  remains 
constant  so  long  as  the  engine  runs  under  constant  conditions. 

The  performance  of  a  steam-engine  is  commonly  stated  in 
pounds  of  steam  per  horse-power  per  hour.  For  example,  a 
small  Corliss  engine,  developing  16.35  horse-power  when 
running  at  61.5  revolutions  per  minute  under  77.4  pounds 
boiler-pressure,  used  548  pounds  of  steam  in  an  hour.  The 
steam  consumption  was 

548  +  16.35  =  33-5 
pounds  per  horse- power  per  hour. 


144  THE    STEAM-ENGINE 

This  method  was  considered  sufficient  in  the  earlier  history 
of  the  steam-engine,  and  may  now  be  used  for  comparing  simple 
condensing  or  non-condensing  engines  which  use  saturated 
steam  and  do  not  have  a  steam-jacket,  for  the  total  heat  of  steam, 
and  consequently  the  cost  of  making  steam  from  water  at  a  given 
temperature  increases  but  slowly  with  the  pressure. 

The  performance  of  steam-engines  may  be  more  exactly 
stated  in  British  thermal  units  per  horse-power  per  minute. 
This  method,  or  some  method  equivalent  to  it,  is  essential  in 
making  comparisons  to  discover  the  advantages  of  superheat- 
ing, steam-jacketing,  and  compounding.  For  example,  the 
engine  just  referred  to  used  steam  containing  two  per  cent  of 
moisture,  so  that  oc1  at  the  steam-pressure  of  77.4  pounds  was 
0.98.  The  barometer  showed  the  pressure  of  the  atmosphere 
to  be  14.7  pounds,  and  this  was  also  the  back-pressure  during 
exhaust.  If  it  be  assumed  that  the  feed-water  was  or  could 
be  heated  to  the  corresponding  temperature  of  2i2°F.,  the 
heat  required  to  evaporate  it  against  77.4  pounds  above  the 
atmosphere  or  92.1  pounds  absolute  was 

xiri  +  9i  ~~  &  ^  °-9^  x  892.2  +  292-2  ~~  I^°-3  =  986.3  B.T.U. 
The  thermal  units  per  horse-power  per  minute  were 

986.3  x  33-5  =  55I^ 

Efficiency  of  the  Actual  Engine.  —  When  the  thermal  units 
per  horse-power  per  minute  are  known  or  can  be  readily  cal- 
culated, the  efficiency  of  the  actual  steam-engine  may  be  found  by 
the  following  method  :  A  horse-power  corresponds  to  the  develop- 
ment of  33000  foot-pounds  per  minute,  which  are  equivalent  to 
33000  -T-  778  =  42.42 

thermal  units.  This  quantity  is  proportional  to  Ql  —  Q2,  and 
the  thermal  units  consumed  per  horse-power  per  minute  are 
proportional  to  Qv  so  that  the  efficiency  is 

-(?«  42.42 


e= 


_  ^ 

Q1  B.T.U.  per  H.P.  per  min.  * 


EFFICIENCY    OF   THE   ACTUAL   ENGINE  145 

For  example,  the  Corliss  engine  mentioned  above  had  an 
efficiency  of 

42.42  -T-  548  =  0.077. 

This  same  method  may  evidently  be  applied  to  any  heat- 
engine  for  which  the  consumption  in  thermal  units  per  horse- 
power per  hour  can  be  applied. 

From  the  tests  reported  in  Chapter  XIII  it  appears  that  the 
engine  in  the  laboratory  of  the  Massachusetts  Institute  of  Tech- 
nology on  one  occasion  used  13.73  pounds  of  steam  per  horse- 
power per  hour,  of  which  10.86  pounds  were  supplied  to  the 
cylinders  and  2.87  pounds  were  condensed  in  steam-jackets  on  the 
cylinders.  The  steam  in  the  supply-pipe  had  the  pressure  of 
157.7  pounds  absolute,  and  contained  1.2  per  cent  of  moisture. 
The  heat  supplied  to  the  cylinders  per  minute  in  the  steam 
admitted  was 

10.86  (x^  +  ql-  q2)  -5-  60 

=  10.86  (0.988  X  859.7  +  333-6  -  126.0)  -s-  60 
=  191  B.T.U.; 

q2  being  the  heat  of  the  liquid  at  the  temperature  of  the  back- 
pressure of  4.5  pounds  absolute. 

The  steam  condensed  in  the  steam-jackets  was  withdrawn 
at  the  temperature  due  to  the  pressure  and  could  have  been 
returned  to  the  boiler  at  that  temperature;  consequently  the 
heat  required  to  vaporize  it  was  rv  and  the  heat  furnished  by 
the  steam  in  the  jackets  was 

2.87  X  0.98  X  859.7  -j-  60  =  40.3  B.T.TJ. 

The  heat  consumed  by  the  engine  was 

191  +  40.3  =231  B.T.U. 

per  horse-power  per  minute,  and  the  efficiency  was 
e  =  42.42  -T-  231  =  0.183. 


146  THE   STEAM-ENGINE 

The  efficiency  of  Carnot's  cycle  for  the  range  of  temperatures 
corresponding  to  157.7  anc^  4-5  pounds  absolute,  namely,  822°.o 
and  6i7°.4  absolute,  is 

T.-  T2     822.0  -  617.4 
e=— *— — 2=-  — '—  =  0.248. 

Tl  822.0 

The  efficiency  for  a  non-conducting  engine  with  complete 
expansion,  calculated  by  equation  (144),  is  for  this  case 

„  #/,  0.824  X  1002.5 

e"  =  i *-* =  i  - -* i—  =  0.227 

rl  +  ql-  q2  859.7  +  333.6  -  126.0 

where  x2  is  calculated  by  the  equation 


= (1.0468  +  0.5192  —  0.2282)  =  0.824. 

1.6235 

During  the  test  in  question  the  terminal  pressure  at  the  end  of 
the  expansion  in  the  low-pressure  cylinder  was  6  pounds  abso- 
lute, which  gives 


(1.0468  +  0.5192  -  0.2476)  =0.834 


1.5012 
and  the  efficiency  by  equation  (148)  was 

-  qc  +  ?,  -  A  (pc  -  /Q  xcu 


e'"  =  i  - 

0.834 X 995. 5  — 138.1  +  126.0  +  111  (6-4.5)  0.834X62 


859-7  +333-6  -126.0 

=  0.222. 

The  real  criterion  of  the  perfection  of  the  action  of  an  engine 
is  the  ratio  of  its  actual  efficiency  to  that  of  a  perfect  engine. 
If  for  the  perfect  engine  we  choose  Carnot's  cycle  the  ratio  is 

e       0.183 

—  = —  =0.736. 

4     0.2485 


EFFICIENCY    OF   THE    ACTUAL    ENGINE  147 

But  if  we  take  for  our  standard  an  engine  with  a  cylinder  of  non- 
conducting material  the  ratio  for  complete  expansion  is 

e        0.183 

—  =  -  *    =  0.807. 
e"      0.227 


For  incomplete  expansion  the  ratio  is 
e       0.18 


0-824- 


To  complete  the  comparison  it  is  interesting  to  calculate 
the  steam-consumption  for  a  non-conducting  steam-engine  by 
equation  (149),  both  for  complete  and  for  incomplete  expan- 
sion. For  complete  expansion  we  have 

60  X  33000 

—  IT"  -  7^  -    -  2  -  ^  —  x  =  IO-5  pounds. 
778  X  0.227  (859-7  +  333-6  -  126.0) 

and  for  incomplete  expansion 

_  60  X  33000 
778  X  o.222  (859-7  +  333-6  -  I26.o)  =  I0" 

per  horse-power  per  hour. 

But  if  these  steam-consumptions  are  compared  with  the 
actual  steam-consumption  of  13.73  pounds  per  horse-power 
per  hour,  the  ratios  are 

10.5  -f-  13.73  =  0.766     and     10.7  •¥  13.73  =  0.783, 

which  are  very  different  from  the  ratios  of  the  efficiencies.  The 
discrepancy  is  due  to  the  fact  that  more  than  a  fourth  of  the 
steam  used  by  the  actual  engine  is  condensed  in  the  jackets 
and  returned  at  full  steam  temperature  to  the  boiler,  while  the 
non-conducting  engine  has  no  jacket,  but  is  assumed  to  use  all 
the  steam  in  the  cylinder. 

From  this  discussion  it  appears  that  there  is  not  a  wide  margin 
for  improvement  of  a  well-designed  engine  running  under  favor- 
able conditions.  Improved  economy  must  be  sought  either  by 
increasing  the  range  of  temperatures  (raising  the  steam-  pressure 


OP    THE 

UNIVERSITY 

OF 


148 


THE    STEAM-ENGINE 


or  improving  the  vacuum),  or  by  choosing  some  other  form  of 
heat-motor,  such  as  the  gas-engine. 

Attention  should  be  called  to  the  fact  that  the  real  criterion  of 
the  economy  of  a  heat-engine  is  the  cost  of  producing  power  by 
that  engine.  The  cost  may  be  expressed  in  thermal  units  per 
horse-power  per  minute,  in  pounds  of  steam  per  horse-power 
per  hour,  in  coal  per  horse-power  per  hour,  or  directly  in  money. 
The  expression  in  thermal  units  is  the  most  exact,  and  the  best 
for  comparing  engines  of  the  same  class,  such  as  steam-engines. 
If  the  same  fuel  can  be  used  for  different  engines,  such  as  steam- 
and  gas-engines,  then  the  cost  in  pounds  of  fuel  per  horse-power 
per  hour  may  be  most  instructive.  But  in  any  case  the  money 
cost  must  be  the  final  criterion.  The  reason  why  it  is  not  more 
frequently  stated  in  reports  of  tests  is  that  it  is  in  many  cases 
somewhat  difficult  to  determine,  and  because  it  is  affected  by 
market  prices  which  are  subject  to  change. 

At  the  present  time  a  pressure  as  high  as  150  pounds  above 
the  atmosphere  is  used  where  good  economy  is  expected.  It 
appears  from  the  table  on  page  132,  showing  the  efficiency  of 
Carnot's  cycle  for  various  pressures,  that  the  gain  in  economy 
by  increasing  steam-pressure  above  150  pounds  is  slow.  The 
same  thing  is  shown  even  more  clearly  by  the  following  table : 

EFFECT   OF    RAISING    STEAM-PRESSURE. 


Non-conducting  Engine. 

Probable  Performance, 
Actual  Engine. 

Boiler- 
pressure  by 
Gauge. 

Efficiency, 
Carnot's  Cycle. 

B.T.U.  per 

B.T.U.  per 

Steam  per 

Efficiency. 

H.P.  per 
Minute. 

H.P.  per 
Minute. 

H.P.  per 
Hour. 

15° 

0.302 

o.  272 

156 

195 

«-S 

200 

0.320 

0.288 

147 

184 

10.5 

300 

°-347 

0.306 

135 

169 

9.6 

In  the  calculations  for  this  table  the  steam  is  supposed  to  be 
dry  as  it  enters  the  cylinder  of  the  engine,  and  the  back-pressure 
is  supposed  to  be  1.5  pounds  absolute,  while  the  expansion  for 
the  non-conducting  engine  is  assumed  to  be  complete.  The 


CONDENSERS  149 

heat-consumption  of  the  non-conducting  engine  is  obtained  by 
dividing  42.42  by  the  efficiency;  thus  for  150  pounds 
42.42  -f-  0.272  =  156. 

The  heat-consumption  of  the  actual  engine  is  assumed  to  be 
one-fourth  greater  than  that  of  the  non-conducting  engine.  The 
steam-consumption  is  calculated  by  the  reversal  of  the  method 
of  calculating  the  thermal  units  per  horse-power  per  minute 
from  the  steam  per  horse- power  per  hour,  and  for  simplicity 
all  of  the  steam  is  assumed  to  be  supplied  to  the  cylinder.  But 
an  engine  which  shall  show  such  an  economy  for  a  given  pressure 
as  that  set  down  in  the  table  must  be  a  triple  or  a  quadruple 
engine  and  must  be  thoroughly  steam- jacketed.  The  actual 
steam-consumption  is  certain  to  be  a  little  larger  than  that  given 
in  the  table,  as  steam  condensed  in  a  steam-jacket  yields  less 
heat  than  that  passed  through  the  cylinder. 

It  is  very  doubtful  if  the  gain  in  fluid  efficiency  due  to  increasing 
steam-pressure  above  150  or  200  pounds  is  not  offset  by  the  greater 
friction  and  the  difficulty  of  maintaining  the  engine.  Higher 
pressures  than  200  pounds  are  used  only  where  great  power  musjt 
be  developed  with  small  weight  and  space,  as  in  torpedo-boats. 

Condensers.  —  Two  forms  of  condensers  are  used  to  condense 
the  steam  from  a  steam-engine,  known  as  jet-condensers  and 
surface-condensers.  The  former  are  commonly  used  for  land 
engines;  they  consist  of  a  receptacle  having  a  volume  equal  to 
one-fourth  or  one-third  of  that  of  the  cylinder  or  cylinders  that 
exhaust  into  it,  into  which  the  steam  passes  from  the  exhaust-pipe 
and  where  it  meets  and  is  condensed  by  a  spray  of  cold  water. 

If  it  be  assumed  that  the  steam  in  the  exhaust-pipe  is  dry 
and  saturated  and  that  it  is  condensed  from  the  pressure  p  and 
cooled  to  the  temperature  tt,  then  the  heat  yielded  per  pound 

of  steam  is  TT 

•tl  —  <?*> 

where  H  is  the  total  heat  of  steam  at  the  pressure  p,  and  qt  is  the 
heat  of  the  liquid  at  the  temperature  tt.  The  heat  acquired  by 
each  pound  of  condensing  or  injection  water  is 


150  THE    STEAM-ENGINE 

where  g*  is  the  heat  of  the  liquid  at  the  temperature  /,  of  the 
injection- water  as  it  enters  the  condenser.  Each  pound  of  steam 
will  require 

G-'+JL=Jb (I50) 

fc-fc 
pounds  of  injection-water. 

For  example,  steam  at  4  pounds  absolute  has  for  the  total 
heat  1126.5.  K  tne  injection- water  enters  with  a  temperature 
of  60°  F.,  and  leaves  with  a  temperature  of  i2o°F.,  then  each 
pound  of  steam  will  require 

r+q  —  qk  _  1126.5  ~  88.0  _ 
qk  -  qi        ~   88.0  -  28.12  "    l7'3 

pounds  of  injection-water.  This  calculation  is  used  only  to 
aid  in  determining  the  size  of  the  pipes  and  passages  leading 
water  to  and  from  the  condenser,  and  the  dimensions  of  the  air- 
pump.  Anything  like  refinement  is  useless  and  impossible, 
as  conditions  are  seldom  well  known  and  are  liable  to  vary. 
From  20  to  30  times  the  weight  of  steam  used  by  the  engine  is 
commonly  taken  for  this  purpose. 

The  jet-condensers  cannot  be  used  at  sea  when  the  boiler- 
pressure  exceeds  40  pounds  by  the  gauge;  all  modern  steamers 
are  consequently  supplied  with  surface-condensers  which  consist 
of  receptacles,  which  are  commonly  rectangular  in  shape,  into 
which  steam  is  exhausted,  and  where  it  is  condensed  on  horizontal 
brass  tubes  through  which  cold  sea-water  is  circulated.  The 
condensed  water  is  drained  out  through  the  air-pump  and  is 
returned  to  the  boiler.  Thus  the  feed-water  is  kept  free  from 
salt  and  other  mineral  matter  that  would  be  pumped  into  the 
boiler  if  a  jet-condenser  were  used,  and  if  the  feed-water  were 
drawn  from  the  mingled  water  and  condensed  steam  from 
such  a  condenser.  Much  trouble  is,  however,  experienced 
from  oil  used  to  lubricate  the  cylinders  of  the  engine,  as  it  is 
likely  to  be  pumped  into  the  boilers  with  the  feed-water,  even 
though  attempts  are  made  to  strain  or  filter  it  from  the  water. 

The  water  withdrawn  from  a  surface-condenser  is  likely  to 


AIR-PUMP 


have  a  different  temperature  from  the  cooling  water  when  it 
leaves  the  condenser.  If  its  temperature  is  tv  then  we  have 
instead  of  equation  (150) 


?*    - 


(isO 


for  the  cooling  water  per  pound  of  steam.  The  difference  is 
really  immaterial,  as  it  makes  little  difference  in  the  actual  value 
of  G  for  any  case. 

Cooling  Surface.  —  Experiments  on  the  quantity  of  cooling 
surface  required  by  a  surface-condenser  are  few  and  unsatis- 
factory, and  a  comparison  of  condensers  of  marine  engines 
shows  a  wide  diversity  of  practice.  Seaton  says  that  with  an 
initial  temperature  of  60°,  and  with  120°  for  the  feed- water,  a 
condensation  of  13  pounds  of  steam  per  square  foot  per  hour 
is  considered  fair  work.  A  new  condenser  in  good  condition 
may  condense  much  more  steam  per  square  foot  per  hour  than 
this,  but  allowance  must  be  made  for  fouling  and  clogging, 
especially  for  vessels  that  make  long  voyages. 

Seaton  also  gives  the  following  table  of  square  feet  of  cooling 
surface  per  indicated  horse- power: 

Absolute  Terminal  Pressure,  Square  Feet 

Pounds  per  Square  Inch.  per  I.  H.  P. 


2O 


10 

8 
6 


17 


•37 


For  ships  stationed  in  the  tropics,  allow  20  per  cent  more; 
for  ships  which  occasionally  visit  the  tropics,  allow  10  per  cent 
more;  for  ships  constantly  in  a  cold  climate,  10  per  cent  less 
may  be  allowed. 

Air-Pump.  —  The  vacuum  in  the  condenser  is  maintained 
by  the  air-pump,  which  pumps  out  the  air  which  finds  its  way 
there  by  leakage  or  otherwise;  the  condensing  water  carries 


152  THE    STEAM-ENGINE 

a  considerable  volume  of  air  into  the  condenser,  and  the  size 
of  the  air-pump  can  be  based  roughly  on  the  average  percentage 
of  air  held  in  solution  in  water;  the  air  which  finds  its  way  into 
a  surface-condenser  enters  mainly  by  leakage  around  the  low- 
pressure  piston-rod  and  elsewhere. 

It  is  customary  to  base  the  size  of  the  air-pump  on  the  dis- 
placement of  the  low-pressure  piston  (or  pistons);  for  example, 
the  capacity  of  a  single-acting  vertical  air-pump  for  a  merchant 
steamer,  with  triple- expansion  engines,  may  be  about  -fa  of  the 
capacity  of  the  low-pressure  cylinder. 

With  the  introduction  of  steam-turbines,  the  importance  of 
a  good  vacuum  becomes  more  marked,  and  the  duty  of  the  air- 
pump,  which  commonly  removes  air  and  also  the  water  of  con- 
densation from  the  condenser,  is  divided  between  'a  dry-air 
pump,  which  removes  air  from  the  condenser,  and  a  water- 
pump,  which  removes  the  water  of  condensation.  Air-pumps 
are  treated  more  at  length  on  page  374,  in  connection  with  the 
discussion  of  compressed  air. 

Designing  Engines.  —  The  only  question  that  is  properly 
discussed  here  is  the  probable  form  of  the  indicator-diagram, 
which  gives  immediately  the  method  of  finding  the  mean  effective 
pressure,  and,  consequently,  the  size  of  the  cylinder  of  the  engine. 
The  most  reliable  way  of  finding  the  expected  mean  effective 
pressure  in  the  design  of  a  new  engine  is  to  measure  an  indicator- 
diagram  from  an  engine  of  the  same  or  similar  type  and  size, 
and  working  under  the  same  conditions. 

If    a    new  engine  varies    so 

p  Boiler  pressure  much  from  the  type  on  which 

the    design    is  based  that  the 
diagram  from  the  latter  cannot 
be  used  directly,  the  following 
^\d  v  method  may  be  used  to  allow 


FIG.  3Sa.  for  moderate  changes  of  boiler 

pressure    or   expansion.      The 

type  diagram  either  on  the  original  card  or  redrawn  to  a  larger 
scale,  may  have  added  to  it  the  axis  of  zero  pressure  and  vol- 


DESIGNING   ENGINES  153 

ume  OF  and  OP  (Fig.  35a).  The  former  is  laid  off  parallel  to 
the  atmospheric  line  and  at  a  distance  to  represent  the  pressure 
of  the  atmosphere,  using  the  scale  for  measuring  pressure  on  the 
diagram.  The  latter  is  drawn  vertical  and  at  a  distance  from  af 
which  shall  bear  the  same  ratio  to  the  length  of  the  diagram  as 
the  clearance  space  of  the  cylinder  has  to  the  piston-displace- 
ment. The  boiler-pressure  line  may  be  drawn  as  shown.  The 
absolute  pressure  may  now  be  measured  from  O  V  with  the  proper 
scale  and  volume  from  OP  with  any  convenient  scale. 

Choosing  points  b  and  c  at  the  beginning  and  end  of  expan- 
sion determine  the  exponent  for  an  exponential  equation  by  the 
method  on  page  66;  do  the  same  for  the  compression  curve  ef. 

Draw  a  diagram  like  Fig.  35  for  the  new  engine,  making  the 
proper  allowance  for  change  of  boiler-pressure  or  point  of  cut- 
off, using  the  probable  clearance  for  determining  the  position 
of  the  line  af.  Allowing  for  loss  of  pressure  from  the  boiler  to 
the  cylinder,  and  for  wire-drawing  or  loss  of  pressure  in  the 
valves  and  passages,  locate  the  points  a  and  b.  The  back- 
pressure line  de  can  be  drawn  from  an  estimate  of  the  probable 
vacuum.  The  volumes  at  c  and  e  are  determined  by  the  action 
of  the  valve  gear.  By  aid  of  the  proper  exponential  equations 
locate  a  few  points  on  be  and  ef  and  sketch  in  those  curves. 
Finish  the  diagram  by  hand  by  comparison  with  the  type  dia- 
gram. If  necessary  draw  two  such  diagrams  for  the  head  and 
crank  ends  of  the  cylinder.  The  mean  effective  pressure  can 
now  be  determined  by  aid  of  the  planimeter  and  used  in  the 
design  of  the  new  engine. 

Usually  the  refinements  of  the  method  just  detailed  are 
avoided,  and  an  allowance  is  made  for  them  in  the  lump  by  a 
practical  factor.  The  following  approximations  are  made: 
(i)  the  pressure  in  the  cylinder  during  admission  is  assumed 
to  be  the  boiler  pressure,  and  during  the  exhaust  the  vacuum 
in  the  condenser;  (2)  the  release  is  taken  to  be  at  the  end  of 
the  stroke;  (3)  both  expansion  and  compression  lines  are  treated 
as  hyperbolae.  The  mean  effective  pressure  is  then  readily 
computed  as  indicated  in  the  following  example. 


154  THE   STEAM-ENGINE 

Problem.  —  Required  the  dimensions  of  the  cylinder  of  an 
engine  to  give  200  horse-power;  revolutions  100;  gauge  pressure 
80  pounds;  vacuum  28  inches;  cut-off  at  i  stroke;  release  at  end 
of  stroke;  compression  at  TV  stroke;  clearance  5  per  cent. 

The  absolute  boiler-pressure  is  94.7  pounds,  and  the  absolute 
pressure  corresponding  to  28  inches  of  mercury  is  nearly  one 
pound.  It  is  convenient  to  take  the  piston  displacement  as 
one  cubic  foot  and  the  stroke  as  one  foot  for  the  purpose  of 
determining  the  mean  effective  pressure.  The  volume  of  cut- 
off is  consequently  i  cubic  foot  due  to  the  motion  of  the  piston 
plus  I&F  cubic  foot  due  to  the  clearance  or  0.35  cubic  foot;  the 
volume  at  release  is  1.05  cubic  foot,  and  at  compression  is  0.15 
cubic  foot. 

The  work  during  admission  (corresponding  to  ab,  Fig.  35a)  is 

94.7  X  144  X  0.35^  foot-pound, 

\ 
and  during  expansion  is 

p,vl  loge^  =  94.7  X  144  X  0.3$  tog,  ^f|. 

The  work  during  exhaust  done  by  the  piston  in  expelling  the 
steam  is 

i  X  144  X  (i  -  o.i), 

and  the  work  during  compression  is 

i  X  144  Xo.i5  loge^- 

O.Os 

The  mean  effective  pressure  in  pounds  per  square  inch  is 
obtained  by  adding  the  first  two  works  and  subtracting  the  last 
two  and  then  dividing  by  144,  so  that 

5^ 
-  i  X  0.9  -  i  X  0.15  log,  =  59.1 


M.E.P.  =  94.7  X  0.25^  +  94.7  X  o.3^1ogfi 


The  probable  mean  effective  pressure  may  be  taken  as 
of  this  computed  pressure,  or  53.2  pounds  per  square  inch. 


DESIGNING   ENGINES 


155 


Given  the  diameter  and  stroke  of  an  engine  together  with  the 
mean  effective  pressure,  and  revolutions,  we  may  find  the  horse- 
power by  the  formula 

2  Uan 


I.H.P.  = 

33000 

where  p  is  the  mean  effective  pressure,  /  is  the  stroke  in  feet,  a  is 
the  area  of  the  circle  for  the  given  diameter  in  square  inches,  and 
n  is  the  number  of  revolutions  per  minute.  For  our  case  we 
may  assume  that  the  stroke  is  twice  the  diameter,  whence 


2  X  53-2  X  —  X  —  X  ioo 
12         4 

33000 
d  =  1 6.8  inches,   s  =  33.6  inches. 


200  = 

33000 


In  practice  the  diameter  would  probably  be  made  i6f  inches 
and  the  stroke  33^-  inches. 


CHAPTER   IX. 


COMPOUND    ENGINES. 

A  COMPOUND  engine  has  commonly  two  cylinders,  one  of 
which  is  three  or  four  times  as  large  as  the  other.  Steam  from 
a  boiler  is  admitted  to  the  small  cylinder,  and  after  doing  work  in 
that  cylinder  it  is  transferred  to  the  large  cylinder,  from  which 
it  is  exhausted,  after  doing  work  again,  into  a  condenser  or 
against  the  pressure  of  the  atmosphere.  If  we  assume  that  the 
steam  from  the  small  cylinder  is  exhausted  into  a  large  receiver, 
the  back-pressure  in  that  cylinder  and  the  pressure  during  the 
admission  to  the  large  cylinder  will  be  uniform.  If,  further,  we 
assume  that  there  is  no  clearance  in  either  cylinder,  that  the 
back-pressure  in  the  small  cylinder  and  the  forward  pressure  in 
the  large  cylinder  are  the  same,  and  that  the  expansion  in  the 
small  cylinder  reduces  the  pressure  down  to  the  back-pressure  in 
that  cylinder,  the  diagram  for  the  small  cylinder  will  be  A  BCD, 


FIG.  36. 


FIG.  37. 


Fig.  36,  and  for  the  large  cylinder  DCFG.  The  volume  in  the 
large  cylinder  at  cut-off  is  equal  to  the  total  volume  of  the  small 
cylinder,  since  the  large  cylinder  takes  from  the  receiver  the  same 
weight  of  s'team  that  is  exhausted  by  the  small  cylinder,  and,  in 
this  case,  at  the  same  pressure. 

The  case  just  discussed  is  one  extreme.     The  other  extreme 
occurs  when  the  small  cylinder  exhausts  directly  into  the  large 

156 


COMPOUND    ENGINES  157 

cylinder  without  an  intermediate  receiver.  In  such  engines  the 
pistons  must  begin  and  end  their  strokes  together.  They  may 
both  act  on  the  beam  of  a  beam  engine,  or  they  may  act  on  one 
crank  or  on  two  cranks  opposite  each  other. 

For  such  an  engine,  ABCD,  Fig.  37,  is  the  diagram  for  the 
small  cylinder.  The  steam  line  and  expansion  line  AB  and  BC 
are  like  those  of  a  simple  engine.  When  the  piston  of  the  small 
cylinder  begins  the  return  stroke,  communication  is  opened  with 
the  large  cylinder,  and  the  steam  passes  from  one  to  the  other, 
and  expands  to  the  amount  of  the  difference  of  the  volume,  it 
being  assumed  that  the  communication  remains  open  to  the  end 
of  the  stroke.  The  back-pressure  line  CD  for  the  small  cylinder, 
and  the  admission  line  HI  for  the  large  cylinder,  gradually  fall 
on  account  of  this  expansion.  The  diagram  for  the  large  cylin- 
der is  HIKG,  which  is  turned  toward  the  left  for  convenience. 

To  combine  the  two  diagrams,  draw  the  line  abed,  parallel  to 
V'OV,  and  from  b  lay  off  bd  equal  to  ca\  then  d  is  one  point  of  the 
expansion  curve  of  the  combined  diagram.  The  point  C  corre- 
sponds with  H,  and  E,  corresponding  with  /,  is  as  far  to  the  right 
as  /  is  to  the  left. 

For  a  non-conducting  cylinder,  the  combined  diagram  for  a 
compound  engine,  whether  with  or  without  a  receiver,  is  the  same 
as  that  for  a  simple  engine  which  has  a  cylinder  the  same  size 
as  the  large  cylinder  of  the  compound  engine,  and  which  takes 
at  each  stroke  the  same  volume  of  steam  as  the  small  cylinder, 
and  at  the  same  pressure.  The  only  advantage  gained  by  the 
addition  of  the  small  cylinder  to  such  an  engine  is  a  more  even 
distribution  of  work  during  the  stroke,  and  a  smaller  initial  stress 
on  the  crank-pin. 

Compound  engines  may  be  divided  into  two  classes  —  those 
with  a  receiver  and  those  without  a  receiver;  the  latter  are  called 
"Woolf  engines  "  on  the  continent  of  Europe.  Engines  without 
a  receiver  must  have  the  pistons  begin  and  end  their  strokes  at 
the  same  time;  they  may  act  on  the  same  crank  or  on  cranks  180° 
apart.  The  pistons  of  a  receiver  compound  engine  may  make 
strokes  in  any  order.  A  form  of  receiver  compound  engine  with 


158  COMPOUND    ENGINES 

two  cylinders,  commonly  used  in  marine  work,  has  the  cranks  at 
90°  to  give  handiness  and  certainty  of  action.  Large  marine 
engines  have  been  made  with  one  small  cylinder  and  two  large 
or  low-pressure  cylinders,  both  of  which  draw  steam  from  the 
receiver  and  exhaust  to  the  condenser.  Such  engines  usually 
have  the  cranks  at  120°,  though  other  arrangements  have  been 
made. 

Nearly  all  compound  engines  have  a  receiver,,  or  a  space 
between  the  cylinders  corresponding  to  one,  and  in  no  case  is 
the  receiver  of  sufficient  size  to  entirely  prevent  fluctuations  of 
pressure.  In  the  later  marine  work  the  receiver  has  been  made 
small,  and  frequently  the  steam-chests  and  connecting  pipes  have 
been  allowed  to  fulfil  that  function.  This  contraction  of  size 
involves  greater  fluctuations  of  pressure,  but  for  other  reasons  it 
appears  to  be  favorable  to  economy. 

Under  proper  conditions  there  is  a  gain  from  using  a  com- 
pound engine  instead  of  a  simple  engine,  which  may  amount  to 
ten  per  cent  or  more.  This  gain  is  to  be  attributed  to  the  division 
of  the  change  of  temperature  from  that  of  the  steam  at  admission 
to  that  of  exhaust  into  two  stages,  so  that  there  is  less  fluctua- 
tion of  temperature  in  a  cylinder  and  consequently  less  inter- 
change of  heat  between  the  steam  and  the  walls  of  the  cylinder. 
Compound  Engine  without  Receiver.  —  The  indicator-dia- 
grams from  a  compound  engine  without  a  receiver  are  repre- 
sented by  Fig.  38.  The  steam  line  and  expan- 
sion line  of  the  small  cylinder,  AB  and  BC,  do 
not  differ  from  those  of  a  simple  engine.  At  C 
the  exhaust  opens,  and  the  steam  suddenly 
expands  into  the  space  between  the  cylinders 
FIG  g  and  the  clearance  of  the  large  cylinder,  and  the 

pressure  falls  from  C  to  D.  During  the  return 
stroke  the  volume  in  the  large  cylinder  increases  more  rapidly 
than  that  of  the  small  cylinder  decreases,  so  that  the  back-press- 
ure line  DE  gradually  falls,  as  does  also  the  admission  line  HI 
of  the  large  cylinder,  the  difference  between  these  two  lines  being 
due  to  the  resistance  to  the  flow  of  steam  from  one  to  the  other. 


COMPOUND    ENGINE   WITH    RECEIVER 


At  E  the  communication  between  the  two  cylinders  is  closed  by 
the  cut-off  of  the  large  cylinder;  the  steam  is  then  compressed 
in  the  small  cylinder  and  the  space  between  the  two  cylinders 
to  F,  at  which  the  exhaust  of  the  small  cylinder  closes;  and  the 
remainder  of  the  diagram  FGA  is  like  that  of  a  simple  engine. 
From  /,  the  point  of  cut-off  of  the  large  cylinder,  the  remainder 
of  the  diagram  IKLMNH  is  like  the  same  part  of  the  diagram 
of  a  simple  engine. 

The  difference  between  the  lines  ED  and  HI  and  the  "  drop  " 
CD  at  the  end  of  the  stroke  of  the  small  piston  indicate  waste 
or  losses  of  efficiency.  The  compression  EFG  and  the  accom- 
panying independent  expansion  IK  in  the  large  cylinder  show  a 
loss  of  power  when  compared  with  a  diagram  like  Fig.  37  for  an 
engine  which  has  no  clearance  or  intermediate  space;  but  com- 
pression is  required  to  fill  waste  spaces  with  steam.  The  com- 
pression EF  is  required  to  reduce  the  drop  CD,  and  the  compres- 
sion FG  fills  the  clearance  in  anticipation  of  the  next  supply  from 
the  boiler.  Neither  compression 
is  complete  in  Fig.  38. 

Diagrams  from  a  pumping  en- 
gine at  Lawrence,  Massachusetts, 
are  shown  by  Fig.  39.  The 
rounding  of  corners  due  to  the 
indicator  makes  it  difficult  to  de- 
termine the  location  of  points  like 
D,  E,  F,  and  /  on  Fig.  38.  The 
low-pressure  diagram  is  taken 
with  a  weak  spring,  and  so  has  an 
exaggerated  height. 

Compound  Engine  with  Receiver.  —  It  has  already  been 
pointed  out  that  some  receiver  space  is  required  if  the  cranks 
of  a  compound  engine  are  to  be  placed  at  right  angles.  When 
the  receiver  space  is  small,  as  on  most  marine  engines,  the  fluc- 
tuations of  pressure  in  the  receiver  are  very  notable.  This  is 
exhibited  by  the  diagrams  in  Fig.  40,  which  were  taken  from  a 
yacht  engine.  An  intelligent  conception  of  the  causes  and  meaning 


FIG.  39. 


j6o  COMPOUND    ENGINES 

of  such  fluctuations  can  be  best  obtained  by  constructing  ideal 
diagrams  for  special  cases,  as  explained  on  page  164. 

Triple  and  Quadruple  Expansion- 
Engines.  —  The  same  influences  which 
introduced  the  compound  engines,  when 
the  common  steam-pressure  changed 
from  forty  to  eighty  pounds  to  the 
square  inch,  have  brought  in  the  succes- 
sive expansion  through  three  cylinders 
FlG' 40t  (the  high-pressure,  intermediate,  and 

low-pressure  cylinders)  now  that  150  to  200  pounds  pressure  are 
employed.  Just  as  three  or  more  cylinders  are  combined  in 
various  ways  for  compound  engines,  so  four,  five,  or  six  cylinders 
have  been  arranged  in  various  manners  for  triple-expansion 
engines;  the  customary  arrangement  has  three  cylinders  with  the 
cranks  at  120°. 

Quadruple  engines  with  four  successive  expansions  have  been 
employed  with  high-pressure  steam,  but  with  the  advisable 
pressures  for  present  use  the  extra  complication  and  friction 
make  it  a  doubtful  expedient. 

Total  Expansion.  —  In  Figs.  36  and  37,  representing  the  dia- 
grams for  compound  engines  without  clearance  and  without 
drop  between  the  cylinders,  the  total  expansion  is  the  ratio  of 
the  volumes  at  E  and  at  B ;  that  is,  of  the  low-pressure  piston  dis- 
placement to  the  displacement  developed  by  the  high-pressure 
piston  at  cut-off.  The  same  ratio  is  called  the  total  or  equiva- 
lent expansion  for  any  compound  engine,  though  it  may  have 
both  clearance  and  drop.  Such  a  conventional  total  expansion 
is  commonly  given  for  compound  and  multiple- expansion  engines, 
and  is  a  convenience  because  it  is  roughly  equal  to  the  ratio  of 
the  initial  and  terminal  pressures;  that  is,  of  the  pressure  at 
cut-off  in  the  high-pressure  cylinder  and  at  release  in  the  low- 
pressure  cylinder.  It  has  no  real  significance,  and  is  not  equiva- 
lent to  the  expansion  in  the  cylinder  of  a  simple  engine,  by  which 
we  mean  the  ratio  of  the  volume  at  release  to  that  at  cut-off,  tak- 
ing account  of  clearance.  And  further,  since  the  clearance  of 


LOW-PRESSURE   CUT-OFF  l6i 

the  high-  and  the  low-pressure  cylinders  are  different  there  can 
be  no  real  equivalent  expansion.  « 

If  the  ratio  of  the  cylinders  is  R  and  the  cut-off  of  the  high- 
pressure  cylinder  is  at  -  of  the  stroke,  then  the  total  expansion 
is  represented  by 

E  =•  eR 

and  I  =  R  +  E. 

e 

This  last  equation  is  useful  in  determining  approximately  the 
cut-off  of  the  high-pressure  cylinder. 

For  example,  if  the  initial  pressure  is  100  pounds  absolute  and 
the  terminal  pressure  is  to  be  10  pounds  absolute,  then  the  total 
expansions  will  be  about  10.  If  the  ratio  of  the  cylinders  is 
3^,  then  the  high-pressure  cut-off  will  be  about 

j  =  3l  •*-  I0  =  °-35 
of  the  stroke. 

Low-pressure  Cut-off.  —  The  cut-off  of  the  low-pressure 
cylinders  in  Figs.  36  and  37  is  controlled  by  the  ratio  of  the 
cylinders,  since  the  volumes  in  the  low-pressure  cylinder  at  cut- 
off is  in  each  case  made  equal  to  the  high-pressure  piston  dis- 
placement; this  is  done  to  avoid  a  drop.  If  the  cut-off  were 
lengthened  there  would  be  a  loss  of  pressure  or  drop  at  the  end 
of  the  stroke  of  the  high-pressure 
piston,  as  is  shown  by  Fig.  41, 
for  an  engine  with  a  large  receiver 
and  no  clearance.  Such  a  drop  will 
have  some  effect  on  the  character  of 
the  expansion  line  C"F  of  the  low- 
pressure  cylinder,  both  for  a  non-con- 
ducting and  for  the  actual  engine 
with  or  without  a  clearance.  Its 
principal  effect  will,  however,  be  on 

the  distribution  of  work  between  the  cylinders;  for  it  is  evident 
that  if  the  cut-off  of  the  low-pressure  cylinder  is  shortened  the 


162  COMPOUND   ENGINES 

pressure  at  C"  will  be  increased  because  the  same  weight  of  steam 
is  taken  in  a  smaller  volume.  The  back-pressure  DC  of  the 
high-pressure  cylinder  will  be  raised  and  the  work  will  be 
diminished;  while  the  forward  pressure  DC"  of  the  low- 
pressure  cylinder  will  be  raised,  increasing  the  work  in  that 
cylinder. 

Ratio  of  Cylinders.  —  In  designing  compound  engines,  more 
especially  for  marine  work,  it  is  deemed  important  for  the  smooth 
action  of  the  engine  that  the  total  work  shall  be  evenly  distributed 
upon  the  several  cranks  of  the  engines,  and  that  the  maximum 
pressure  on  each  of  the  cranks  shall  be  the  same,  and  shall  not 
be  excessive.  In  case  two  or  more  pistons  act  on  one  crank, 
the  total  work  and  the  resultant  pressure  on  those  pistons  are 
to  be  considered;  but  more  commonly  each  piston  acts  on  a 
separate  crank,  and  then  the  work  and  pressure  on  the  several 
pistons  are  to  be  considered. 

In  practice  both  the  ratio  of  the  cylinders  and  the  total  expan- 
sions are  assumed,  and  then  the  distribution  of  work  and  the 
maximum  loads  on  the  crank-pins  are  calculated,  allowing  for 
clearance  and  compression.  Designers  of  engines  usually  have 
a  sufficient  number  of  good  examples  at  hand  to  enable  them 
to  assume  these  data.  In  default  of  such  data  it  may  be  neces- 
sary to  assume  proportions,  to  make  preliminary  calculations, 
and  to  revise  the  proportions  till  satisfactory  results  are  obtained. 
For  compound  engines  using  80  pounds  steam-pressure  the  ratio 
is  i :  3  or  i :  4.  For  triple-expansion  engines  the  cylinders  may 
be  made  to  increase  in  the  ratio  i :  2  or  i :  2\. 

Approximate  Indicator- Diagrams.  —  The  indicator-diagrams 
from  some  compound  and  multiple- expansion  engines  are  irreg- 
ular and  apparently  erratic,  depending  on  the  sequence  of  the 
cranks,  the  action  of  the  valves,  and  the  relative  volumes  of  the 
cylinders  and  the  receiver  spaces.  A  good  idea  of  the  effects  and 
relations  of  these  several  influences  can  be  obtained  by  making 
approximate  calculations  of  pressures  at  the  proper  parts  of  the 
diagrams  by  a  method  which  will  now  be  illustrated. 

For  such  a  calculation  it  will  be  assumed  that  all  expansion 


DIRECT-EXPANSION    ENGINE  163 

lines  are  rectangular  hyperbolae,  and  in  general  that  any  change 
of  volume  will  cause  the  pressure  to  change  inversely  as  the 
volume.  Further,  it  will  be  assumed  that  when  communication 
is  opened  between  two  volumes  where  the  pressures  are  different, 
the  resultant  pressure  may  be  calculated  by  adding  together  the 
products  of  each  volume  by  its  pressure,  and  dividing  by  the  sum 
of  the  volumes.  Thus  if  the  pressure  in  a  cylinder  having  the 
volume  vc  is  pc,  and  if  the  pressure  is  pr  in  a  receiver  where 
the  volume  is  vri  then  after  the  valve  opens  communication  from 
the  cylinder  to  the  receiver  the  pressure  will  be 

peve  +  prvr 
vc  +  vr 

The  same  method  will  be  used  when  three  volumes  are  put  into 
communication. 

It  will  be  assumed  that  there  are  no  losses  of  pressure  due  to 
throttling  or  wire-drawing;  thus  the  steam  line  for  the  high- 
pressure  cylinder  will  be  drawn  at  the  full  boiler-pressure,  and 
the  back-pressure  line  in  the  low-pressure  cylinder  will  be  drawn 
to  correspond  with  the  vacuum  in  the  condenser.  Again,  cylin- 
ders and  receiver  spaces  in  communication  will  be  assumed  to 
have  the  same  pressure. 

For  sake  of  simplicity  the  motions  of  pistons  will  be  assumed 
to  be  harmonic. 

Diagrams  constructed  in  this  way  will  never  be  realized  in 
any  engine;  the  degree  of  discrepancy  will  depend  on  the  type 
of  engine  and  the  speed  of  rotation.  For  slow-speed  pumping- 
engines  the  discrepancy  is  small  and  all  irregularities  are  easily 
accounted  for.  On  the  other  hand  the  discrepancies  are  large 
for  high-speed  marine-engines,  and  for  compound  locomotives 
they  almost  prevent  the  recognition  of  the  events  of  the  stroke. 

Direct- expansion  Engine.  —  If  the  two  pistons  of  a  compound 
engine  move  together  or  in  opposite  directions  the  diagrams 
are  like  those  shown  by  Fig.  42.  Steam  is  admitted  to  the  high- 
pressure  cylinder  from  a  to  b\  cut-off  occurs  at  b,  and  be  repre- 
sents expansion  to  the  end  of  the  stroke;  be  being  a  rectangular 


1 64 


COMPOUND   ENGINES 


hyperbola  referred  to  the  axes  OF  and  OP,  from  which  a,  b,  and 
c  are  laid  off  to  represent  absolute  pressures  and  volumes,  includ- 
ing clearance. 


p    P 


o    o' 


FIG.  42. 

At  the  end  of  the  stroke  release  from  the  high-pressure 
cylinder  and  admission  to  the  low-pressure  cylinder  are  assumed 
to  take  place,  so  that  communication  is  opened  from  the  high- 
pressure  cylinder  through  the  receiver  space  into  the  low-press- 
ure cylinder.  As  a  consequence  the  pressure  falls  from  c  to  d, 
and  rises  from  n  to  h  in  the  low-pressure  cylinder.  The  line 
O'P'  is  drawn  at  a  distance  from  OP,  which  corresponds  to  the 
volume  of  the  receiver  space,  and  the  low-pressure  diagram  is 
referred  to  O'P'  and  O'F'  as  axes. 

The  communication  between  the  cylinders  is  maintained  until 
cut-off  occurs  at  i  for  the  low-pressure  cylinder.  The  lines  de 
and  hi  represent  the  transfer  of  steam  from  the  high-pressure 
to  the  low-pressure  cylinder,  together  with  the  expansion  due  to 
the  increased  size  of  the  large  cylinder.  After  the  cut-off  at  i, 
the  large  cylinder  is  shut  off  from  the  receiver,  and  the  steam  in 
it  expands  to  the  end  of  the  stroke.  The  back-pressure  and 
compression  lines  for  that  cylinder  are  not  affected  by  compound- 
ing, and  are  like  those  of  a  simple  engine.  Meanwhile  the  small 
piston  compresses  steam  into  the  receiver,  as  represented  by 
ef,  till  compression  occurs,  after  which  compression  into  the 
clearance  space  is  represented  by/g.  The  expansion  and  com- 
pression lines  ik  and  mn  are  drawn  as  hyperbolae  referred  to  the 
axes  O'P'  and  O'  Vr.  The  compression  line  ef  is  drawn  as  an  hyper- 
bola referred  to  O'F  and  O'P',  while/g  is  referred  to  OF  and  OP. 


DIRECT-EXPANSION    ENGINE  165 

In  Fig.  42  the  two  diagrams  are  drawn  with  the  same  scale 
for  volume  and  pressure,  and  are  placed  so  as  to  show  to  the 
eye  the  relations  of  the  diagrams  to  each  other.  Diagrams 
taken  from  such  an  engine  resemble  those  of  Fig.  39,  which 
have  the  same  length,  and  different  vertical  scales  depending 
on  the  springs  used  in  the  indicators. 

Some  engines  have  only  one  valve  to  give  release  and  com- 
pression for  the  high-  pressure  cylinder  and  admission  and  cut- 
off for  the  low-pressure  cylinder.  In  such  case  there  is  no 
receiver  space,  and  the  points  e  and  /coincide. 

When  the  receiver  is  closed  by  the  compression  of  the  high- 
pressure  cylinder  '  it  is  filled  with  steam  with  the  pressure  repre- 
sented by  /.  It  is  assumed  that  the  pressure  in  the  receiver 
remains  unchanged  till  the  receiver  is  opened  at  the  end  of  the 
stroke.  It  is  evident  that  the  drop  cd  may  be  reduced  by  short- 
ening the  cut-off  of  the  low-pressure  cylinder  so  as  to  give  more 
compression  from  e  to  f  and  consequently  a  higher  pressure  at 
/  when  the  receiver  is  closed. 

Representing  the  pressure  and  volume  at  the  several  points 
by  p  and  v  with  appropriate  subscript  letters,  and  represent- 
ing the  volume  of  the  receiver  by  vr,  we  have  the  following 
equations  : 

Pa  =  pb  =  initial  pressure; 
PI  =  Pm  =  back-  pressure; 

PC  =  PbVb    +   Vc', 

Pn  =  PmVm    •*•  Vn; 

Pd  =  Ph  =    (Mr    +  M*    +  Pf^r)    +    (Ve    +  Vn    +  Vr)\ 

Pe   =  Pi  =   Pd    (Ve    +  Vn    +  Vr)    -4-    (Ve    +  V{   +  IV); 

pf  =  pe  (ve  +vr)  -5-  (vf  +-z;r); 
Pg  =  Pfvf  •*•  vff'> 

Pk  =   PiVi   +  Vk. 


The  pressures  pc  and  pn  can  be  calculated  directly.  Then  the 
equations  for  pd,  pe,  and  pf  form  a  set  of  three  simultaneous 
equations  with  three  unknown  quantities,  which  can  be  easily 
solved.  Finally,  py  and  pk  may  be  calculated  directly. 


166  COMPOUND    ENGINES 

For  example,  let  us  find  the  approximate  diagram  for  a  direct- 
expansion  engine  which  has  the  low-pressure  piston  displacement 
equal  to  three  times  the  high-pressure  piston  displacement. 
Assume  that  the  receiver  space  is  half  the  smaller  piston  dis- 
placement, and  that  the  clearance  for  each  cylinder  is  one-tenth 
of  the  corresponding  piston  displacement.  Let  the  cut-off  for 
each  cylinder  be  at  half-stroke,  and  the  compression  at  nine- 
tenths  of  the  stroke;  let  the  admission  and  release  be  at  the  end 
of  the  stroke.  Let  the  initial  pressure  be  65.3  pounds  by  the 
gauge  or  80  pounds  absolute,  and  let  the  back-pressure  be  two 
pounds  absolute. 

If  the  volume  of  the  high-pressure  piston  displacement  be 
taken  as  unity,  then  the  several  required  volumes  are: 

vb  =  0.5  +  o.i  =0.6  vh  =  vn  =  3  X  o.i  =  0.3 

vc  ==  vd  =  i.o  +  o.i  =  i.i       V{  =  3  (0.5  +  o.i)  =  1.8 
ve  =  0.5  +  o.i  =  0.6  vt  =  v(  =  3  (i.o  +  o.i)  =  3.3 

Vf   =  O.I    +  O.I    =   0.2  Vm  =   3   (O.I    +  O.i)   =  0.6 

Vg      =      O.I  Vr      =      0.5 

The  pressures  may  be  calculated  as  follows: 

pa  =  pb  =  80;    pt  =  pm  =  2; 

PC  =  p*Vb  -*-  vc  =  80  X  0.6  -f-  i.i  =  43.6; 

Pn  =   PmVm    -4-  Vn  =    2    X  0.6    -v-  0.3   =   4J 

Pe    =  Pd    (Ve   +  Vn   +  Vr)  -5-  K   +  ^  +  Vr)   =  Pd  (l-I    +  0.3    +  0.5) 

-r-  (0.6  +  1.8  +  0.5)  =  0.655  Pd\ 

P/   =  Pe  (Ve    +  Vr)    +    (ty   +  Vr)   =   pe  (o.6    +0.5)    -v-    (o.2    +   0.5) 

=  1.57  pe   =  1.57  X  0.655  Pd  =  1-03  Pd', 

Pd  =    (PcVc    +  pnV»    +  p/Ur)    +    (Vc    +  Vn    +  Vr) 

=  (80  X  0.6  +  4  X  0.3  -f  0.5  pf)  -v-  (0.6  +  0.3  +  0.5) 

=  25.89  +  0.26  pf\ 

pd  =  25.89  -1-  0.26  X  1.03  pd\     pd  =  35.36; 
p.  =  pi  =  0.655  Pd  =  0.655  X  35.36  =  23.2; 
Pf  =  I-°3  P*  =  i-03  X  35-36  =  36.5; 
Pg  =  Pfvf  +'u,=*  36.5   X  0.2  +  o.i  =  73; 
Pt  =  M-  "*•  v*  =  23-2  X  1.8  -^  3.3  =  12.6. 


DIRECT-EXPANSION    ENGINE  167 

As  the  pressures  and  volumes  are  now  known  the  diagrams 
of  Fig.  42  may  be  drawn  to  scale.  Or,  if  preferred,  diagrams 
like  Fig.  39  may  be  drawn,  making  them  of  the  same  length  and 
using  convenient  vertical  scales  of  pressure.  If  the  engine  runs 
slowly  and  has  abundant  valves  and  passages  the  diagrams 
thus  obtained  will  be  very  nearly  like  those  taken  from  the  engine 
by  indicators.  If  losses  of  pressure  in  valves  and  passages  are- 
allowed  for,  a  closer  approximation  can  be  made. 

The  mean  effective  pressures  of  the  diagrams  may  be  readily 
obtained  by  the  aid  of  a  planimeter,  and  may  be  used  for  esti- 
mating the  power  of  the  engine.  For  this  purpose  we  should 
either  use  the  modified  diagrams  allowing  for  losses  of  pressure, 
or  we  should  affect  the  mean  effective  pressures  by  a  multiplier 
obtained  by  comparison  of  the  approximate  with  the  actual  dia- 
grams from  engines  of  the  same  type.  For  a  slow-speed  pump- 
ing-engine  the  multiplier  may  be  as  large  as  0.9  or  even  more; 
for  high-speed  engines  it  may  be  as  small  as  0.6. 

The  mean  effective  pressures  of  the  diagrams  may  be  calcu- 
lated from  the  volumes  and  pressures  if  desired,  assuming,  of 
course,  that  the  several  expansion  and  compression  curves  are 
hyperbolae.  The  process  can  be  best  explained  by  applying  it 
to  the  example  already  considered.  Begin  by  finding  the  mean 
pressure  during  the  transfer  of  steam  from  the  high-pressure 
cylinder  to  the  low-pressure  cylinder  as  represented  by  de  and  hi. 
The  net  effective  work  during  the  transfer  is 


=    144  Pd  (V* 


=    144  X  35-4  (i-i  +  0.3  +  0.5) 


=  4120  foot-pounds 

for  each  cubic  foot  of  displacement  of  the  high-pressure  piston. 
This  corresponds  with  our  previous  assumption  of  unity  for  the 
displacement  of  that  piston.  The  increase  of  volume  is 

=0.6+1.8+0.5-    (l.I+0.3+0.5)  =  i; 


l68  COMPOUND    ENGINES 

so  that  the  mean  pressure  during  the  transfer  is 
4120-7-1  X  144  =  28.6  =  px 

pounds  per  square  inch,  which  acts  on  both  the  high-  and  the 
low-pressure  pistons. 

The  effective  work  for  the  small  cylinder  is  obtained  by  add- 
ing the  works  under  ab  and  be  and  subtracting  the  works  under 
de,  ef,  and/g.  So  that 

WH  =   144     \pa  (V  —  V«)    +  pbVt  log.^  -  pm  (Vd  -  V.) 

-  p.(v.  + 


144     80  (0.6  -  o.i)  +  80  X  0.6  log,  —•-  28.6  (i.i  -  0.6) 

o.o 


=  144  X  33.26  =  4789  foot-pounds. 

This  is  the  work  for  each  cubic  foot  of  the  high-pressure  piston 
displacement,  and  the  mean  effective  pressure  on  the  small  piston 
is  evidently  33.26  pounds  per  square  inch. 

In  a  like  manner  the  work  of  the  large  piston  is 

Wl    =  144     \pm(Vt  —  V»)  +  piVtloge  —    —  pi  (Vi  —  Vm)  —  pmVm  log»~"* 

=  144    1  28.6  (1.8  -  0.3)  +  23.2  X  1.8  log.  ^f 

(  1.5 

—  2  (3.3  —  0.6)  —  2  X  o.61oga  ~^-l  =  144  X  61.92  =  8916  foot-pounds. 

Since  the  ratio  of  the  piston  displacements  is  3,  the  work  for 
each  cubic  foot  of  the  low-pressure  piston  displacement  is  one-third 
of  the  work  just  calculated;  and  the  mean  effective  pressure  on 
the  large  piston  is 

61.92  -?-  3  =  20.64 

pounds  per  square  inch. 

The  proportions  given  in  the  example  lead  to  a  very  uneven 
distribution  of  work;  that  of  the  large  cylinder  being  nearly 
twice  as  much  as  is  developed  in  the  small  cylinder.  The  dis- 


CROSS-COMPOUND   EWGINE 


169 


tribution  can  be  improved  by  lengthening  the  cut-off  of  the 
large  cylinder,  or  by  changing  the  proportions  of  the  engine. 

As  has  already  been  pointed  out,  the  works  just  calculated 
and  the  corresponding  mean  effective  pressures  are  in  excess 
of  those  that  will  be  actually  developed,  and  must  be  affected 
by  multipliers  which  may  vary  from  0.6  to  0.9,  depending  on 
the  type  and  speed  of  the  engine. 

Cross- compound  Engine.  —  A  two-cylinder  compound  engine 
with  pistons  connected  to  cranks  at  right  angles  with  each  other 
is  frequently  called  a  cross-compound  engine.  Unless  a  large 
receiver  is  placed  between  the  cylinders  the  pressure  in  the  space 
between  the  cylinders  will  vary  widely. 

Two  cases  arise  in  the  discussion  of  this  engine  according  as 


FIG.  43- 


the  cut-off  of  the  large  cylinder  is  earlier  or  later  than  half-stroke; 
in  the  latter  case  there  is  a  species  of  double  admission  to  the 
low-pressure  cylinder,  as  is  shown  in  Fig.  43.  For  sake  of 
simplicity  the  release,  and  also  the  admission  for  each  cylinder, 
is  assumed  to  be  at  the  end  of  the  stroke.  If  the  release  is  early 
the  double  admission  occurs  before  half-stroke. 

The  admission  and  expansion  of  steam  for  the  high-pressure 
cylinder  are  represented  by  ab  and  be.  At  c  release  occurs, 
putting  the  small  cylinder  in  communication  with  the  inter- 
mediate receiver,  which  is  then  open  to  the  large  cylinder.  There 
is  a  drop  at  cd  and  a  corresponding  rise  of  pressure  mn  on  the 
large  piston,  which  is  then  at  half-stroke;  it  will  be  assumed 
that  the  pressures  at  d  and  at  n  are  identical.  From  d  to  e  the 


170  COMPOUND    ENGINES 

steam  is  transferred  from  the  small  to  the  large  cylinder,  and 
the  pressure  falls  because  the  volume  increases;  no  is  the  corre- 
sponding line  on  the  low-pressure  diagram.  The  cut-off  at  o 
for  the  large  cylinder  interrupts  this  transfer,  and  steam  is  then 
compressed  by  the  small  piston  into  the  intermediate  receiver 
with  a  rise  of  pressure  as  represented  by  ef.  The  admission  to 
the  large  cylinder,  tk,  occurs  when  the  small  piston  is  at  the 
middle  of  its  stroke,  and  causes  a  drop,  fg,  in  the  small  cylinder. 
From  g  to  h  steam  is  transferred  through  the  receiver  from  the 
small  to  the  large  cylinder.  The  pressure  rises  at  first  because 
the  small  piston  moves  rapidly  while  the  large  one  moves  slowly 
until  its  crank  gets  away  from  the  dead-point;  afterwards  the 
pressure  falls.  The  line  kl  represents  this  action  on  the  low- 
pressure  diagram.  At  h  compression  occurs  for  the  small 
cylinder,  and  hi  shows  the  rise  of  pressure  due  to  compression. 
For  the  large  cylinder  the  line  Im  represents  the  supply  of  steam 
from  the  receiver,  with  falling  pressure  which  lasts  till  the  double 
admission  at  mn  occurs. 

The  expansion,  release,  exhaust,  and  compression  in  the  large 
cylinder  are  not  affected  by  compounding. 

Strictly,  the  two  parts  of  the  diagram  for  the  low-pressure 
cylinder,  mnopq  and  stklm,  belong  to  opposite  ends  of  the  cylin- 
der, one  belonging  to  the  head  end  and  one  to  the  crank  end. 
With  harmonic  motion  the  diagrams  from  the  two  ends  are 
identical,  and  no  confusion  need  arise  from  our  neglect  to  deter- 
mine which  end  of  the  large  cylinder  we  are  dealing  with  at  any 
time.  Such  an  analysis  for  the  two  ends  of  the  cylinder,  taking 
account  of  the  irregularity  due  to  the  action  of  the  connecting- 
rod,  would  lead  to  a  complexity  that  would  be  unprofitable. 

A  ready  way  of  finding  corresponding  positions  of  two  pistons 
connected  to  cranks  at  right  angles  with  each  other  is  by  aid 
of  the  diagram  of  Fig.  44.  Let  O  be  the  centre  of  the  crank- 
shaft and  pRyRxq  be  the  path  of  the  crank-pin.  When  one  piston 
has  the  displacement  py  and  its  crank  is  at  ORy,  the  other  crank 
may  be  90°  ahead  at  ORX  and  the  corresponding  piston  displace- 
ment will  be  px.  The  same  construction  may  be  used  if  the 


CROSS-COMPOUND   ENGINE 


171 


crank  is  90°  behind  or  if  the  angle  RyORx  is  other  than  a  right 
angle.  The  actual  piston  position  and  crank  angles  when 
affected  by  the  irregularity  due  to  the 
connecting-rod  will  differ  from  those  found 
by  this  method,  but  the  positions  found 
by  such  a  diagram  will  represent  the  aver- 
age positions  very  nearly. 

The  several  pressures  may  be  found  as 
follows :  FIG. 

pb  —  Pa  =  initial  pressure; 
ps  =  pq  =  back-pressure; 


ft  £  S      S         '  t J 

Pd   ==    Pn   ==    )  Pc^c    ~t~   Pm  \  ^m.    ~\~  ^r )  I     ~^~    \^ c    ~f~  V      ~\~  1)» 
Pe  =  Po  =  Pd    (Ve   +Vm+  Vr)    +   (Ve    +V0   +  Vr); 
Pf  =   Pe    (Ve    +  Vr)    -4-    (Vf  +  Vr); 
Pg  =   Pk  =  Ipf  (Vf  +  Vr)    +  ptVt]    -f-   (Vf+  Vt   +  Vr); 

Pm=  Pi  (Vi   +  Vr)    +    (Vm   +  Vr)j 
Pi   = 


The  pressures  pc  and  />„  can  be  found  directly  from  the  initial 
pressure  and  the  back-pressure,  and  finally  the  last  two  equa- 
tions give  direct  calculations  for  pi  and  pp  so  soon  as  ph  and  p0 
are  found.  There  remain  six  equations  containing  six  unknown 
quantities,  which  can  be  readily  solved  after  numerical  values 
are  assigned  to  the  known  pressures  and  to  all  the  volumes. 

The  expansion  and  compression  lines,  be  and  hi,  for  the  high- 
pressure  diagrams  are  hyperbolae  referred  to  the  axes  OV  and 
OP;  and  in  like  manner  the  expansion  and  compression  lines  op 
and  st,  for  the  low-pressure  diagram,  are  hyperbolae  referred  to 
O'V  and  OfPr.  The  curve  <?/is  an  hyperbola  referred  to  Of  V  and 
O'P',  and  the  curve  Im  is  an  hyperbola  referred  to  OV'  and 
OP.  The  transfer  lines  de  and  no,  gh  and  kl,  are  not  hyper- 
bolae. They  may  be  plotted  point  by  point  by  finding  corre- 


172  COMPOUND    ENGINES 

spending  intermediate  piston  positions,  px  and  pv,  by  aid  of  Fig. 
44,  and  then  calculating  the  pressure  for  these  positions  by  the 
equation 

P*  =   Pv  =   Pd    (Vd    +  Vm    +  Vr)     •*•    (V,    +  Vy    +  Vr)- 

The  work  and  mean  effective  pressure  may  be  calculated  in  a 
manner  similar  to  that  given  for  the  direct-expansion  engine; 
but  the  calculation  is  tedious,  and  involves  two  transfers,  de  and 
no,  and  gh  and  kl.  The  first  involves  only  an  expansion,  and 
presents  no  special  difficulty;  the  second  consists  of  a  compres- 
sion and  an  expansion,  which  can  be  dealt  with  most  conveniently 
by  a  graphical  construction.  All  things  considered,  it  is  better 
to  plot  the  diagrams  to  scale  and  determine  the  areas  and  mean 
effective  pressures  by  aid  of  a  planimeter. 

If  the  cut-off  of  the  low-pressure  is  earlier  than  half-stroke  so 
as  to  precede  the  release  of  the  high-pressure  cylinder  the  transfer 
represented  by  de  and  no,  Fig.  43,  does  not  occur.  Instead  there 
is  a  compression  from  dtof  and  an  expansion  from  /  to  m.  The 
number  of  unknown  quantities  and  the  number  of  equations  are 
reduced.  On  the  other  hand,  a  release  before  the  end  of  the 
stroke  of  the  high- pressure  piston  requires  an  additional  unknown 
quantity  and  one  more  equation. 

Triple  Engines.  —  The  diagrams  from  triple  and  other  mul- 
tiple-expansion engines  are  likely  to  show  much  irregularity,  the 
form  depending  on  the  number  and  arrange- 
ment of  the  cylinders  and  the  sequence  of  the 
cranks.  A  common  arrangement  for  a  triple 
engine  is  to  have  three  pistons  acting  on 
cranks  set  equidistant  around  the  circle,  as 
shown  by  Fig.  45.  Two  cases  arise  depending 
on  the  sequence  of  the  cranks,  which  may  be 
in  the  order,  from  one  end  of  the  engine,  of 
high-pressure,  low-pressure,  and  intermediate,  as  shown  by  Fig. 
45;  or  in  the  order  of  high- pressure,  intermediate,  and  low- 
pressure. 

With  the  cranks  in  the  order,  high-pressure,  low-pressure,  and 


TRIPLE    ENGINES 


173 


intermediate,  as  shown  by  Fig.  45,  the  diagrams  are  like  those 
given  by  Fig.  46.  The  admission  and  expansion  for  the  high- 
pressure  cylinder  are  represented  by  abc.  When  the  high- 
pressure  piston  is  at  release,  its  crank  is  at  H,  Fig.  45,  and  the 
intermediate  crank  is  at  /,  so  that  the  intermediate  piston  is 
near  half-stroke.  If  the  cut-off  for  that  cylinder  is  later  than 


Scale  160 


Atmospheric  line 


i          i 

Atmospheric  line     j 

y 

^"^•^^  !' 

Sdale  40 

€ 

FIG.  46. 


half-stroke,  it  is  in  communication  with  the  first  receiver  when 
its  crank  is  at  /,  and  steam  may  pass  through  the  first  receiver 
from  the  high-pressure  to  the  intermediate  cylinder,  and  there  is 
a  drop  cd,  and  a  corresponding  rise  of  pressure  no  in  the  inter- 
mediate cylinder.  The  transfer  continues  till  cut-off  for  the 


COMPOUND    ENGINES 

intermediate  cylinder  occurs  at  p,  corresponding  to  the  piston 
position  e  for  the  high-pressure  cylinder.  From  the  position  e 
the  high-  pressure  piston  moves  to  the  end  of  the  stroke  at  /, 
causing  an  expansion,  and  then  starts  to  return,  causing  the 
compression  fg.  When  the  high-pressure  piston  is  at  g  the 
intermediate  cylinder  takes  steam  at  the  other  end,  causing  the 
drop  gh  and  the  rise  of  pressure  xl.  Then  follows  a  transfer  of 
steam  from  the  high-pressure  to  the  intermediate  cylinder  repre- 
sented by  hi  and  Im.  At  i  the  high-pressure  compression  ik 
begins,  and  is  carried  so  far  as  to  produce  a  loop  at  k.  After 
compression  for  the  high-pressure  cylinder  shuts  it  from  the 
first  receiver,  the  steam  in  that  receiver  and  in  the  intermediate 
cylinder  expands  as  shown  by  mn.  The  expansion  in  the  inter- 
mediate cylinder  is  represented  by  pq  and  the  release  by  qr, 
corresponding  to  a  rise  of  pressure  a/9  in  the  low-pressure  cylin- 
der. rs  and  /?7  represent  a  transfer  of  steam  from  the  inter- 
mediate cylinder  to  the  low-pressure  cylinder.  The  remainder 
of  the  back-pressure  line  of  the  intermediate  cylinder  and  the 
upper  part  of  the  low-pressure  diagram  for  the  low-pressure 
cylinder  correspond  to  the  same  parts  of  the  high-pressure  and 
the  intermediate  cylinders,  so  that  a  statement  of  the  actions  in 
detail  does  not  appear  necessary. 

The  equations  for  calculating  the  pressure  are  numerous,  but 
they  are  not  difficult  to  state,  and  the  solution  for  a  given  exam- 
ple presents  no  special  difficulty.  Thus  we  have 

pa  =  pb  =  initial  pressure;  vp  =  vol.  first  receiver; 

pe  =  pbv6  -±-ve\  VR=  v°l-  second  receiver; 

I.  pd  =  p0  =  \  peVe  +  pn  (v0+Vp)  |  -T-  (vd  +v0 
P'  =  PP  =  pd(vd  +  v0  +  vp)  -f-  (v,  +  vp  + 

pf   =   p,    (V,  +    Vp  )     -r-    (Vf+    Vp}', 

Pa  = 


.  II.  ph  =  pi  =\p0  (vg  +  vp)  +  pmvm\  -f- 


pk  =  pM  -5-  vie  ; 

pn  =   pm  (Vm,  +   Vp)  +   (Vn  + 

Pi  =  ppv*  +  vq  ; 


TRIPLE   ENGINES 


175 


Pt=Py  =  Pr  (Vr  +  Va  +  V 

#i  =  £«  K  +  v*>  -  (Vt  + 

Pu  =  Pt  (Vt  +  v*>  +  (v.  + 


IV.    p,  =    \p*  (V*  +  VR)  +  pr,Vr,l    -*•   (V.  + 

/».=  #.  (v.  +  v,  +  7^)  -5-  (vw  +  v,  +  Vj); 
/>.  =  #»v«  H-  v.; 

/>.  =   (V.  +  Vjj)  -i-   (Va  +  Vjj); 
/>*  =  pyVy  -4-  V5; 

pe  =  p.  =  back-  pressure; 


The  pressures  at  c  and  at  ij  can  be  calculated  immediately 
from  the  initial  pressure  and  from  the  back-pressure.  Then  it 
will  be  recognized  that  there  are  four  individual  equations  for 
finding  pf,  pt,  pt,  and  pt.  The  fourteen  remaining  equations, 
solved  as  simultaneous  equations,  give  the  corresponding  four- 
teen required  pressures,  some  of  which  are  used  in  calculating 
the  four  pressures  which  are  determined  by  the  four  individual 
equations.  The  most  ready  solution  may  be  made  by  contin- 
uous substitution  in  the  four  equations  which  are  numbered  at  the 
left  hand.  Thus  for  pg  in  equation  II,  we  may  substitute, 


VP 


In  the  actual  computation  the  several  volumes  and  the  proper 
sums  of  volumes  are  to  be  first  determined;  consequently  the 
factors  following  pd  will  be  numerical  factors  which  may  be  con- 
veniently reduced  to  the  lowest  terms  before  introduction  in  the 
equation.  This  system  of  substitution  will  give  almost  immedi- 
ately four  equations  with  four  unknown  quantities  which  may 
readily  be  solved;  after  which  the  determination  of  individual 
pressures  will  be  easy.  In  handling  these  equations  the  letters 
representing  smaller  pressures  should  be  eliminated  first,  thus 
giving  values  of  higher  pressure  like  pd  to  tenths  of  a  pound; 
afterward  the  lower  pressure  can  be  determined  to  a  like  degree 


176  COMPOUND   ENGINES 

of  accuracy.  A  skilled  computer  may  make  a  complete  solu- 
tion of  such  a  problem  in  two  or  three  hours,  which  is  not  exces- 
sive for  an  engineering  method. 

If  the  cut-off  for  the  intermediate  cylinder  occurs  before  the 
release  of  the  high-pressure  cylinder,  then  the  transfer  represented 
by  de  and  op  does  not  occur.  In  like  manner,  if  the  cut-off  for 
the  low-pressure  cylinder  occurs  before  the  release  for  the  inter- 
mediate cylinder,  the  transfer  represented  by  rs  and  /ty  does 
not  occur.  The  omission  of  a  transfer  of  course  simplifies  the 
work  of  deducing  and  of  solving  equations. 

In  much  the  same  way,  equations  may  be  deduced  for  cal- 
culating pressures  when  the  cranks  have  the  sequence  high- 
pressure,  intermediate,  and  low-pressure.  The  diagrams  take 
forms  which  are  distinctly  unlike  those  for  the  other  sequence  of 
cranks.  In  general,  the  case  solved,  i.e.,  high-pressure,  low- 
pressure,  and  intermediate,  gives  a  smoother  action  for  the 
engine. 

For  example,  the  engines  of  the  U.  S.  S.  Machias  have  the 
following  dimensions  and  proportions: 

High-  Inter-  Low- 

pressure,         mediate,      pressure. 

Diameter  of  piston,  inches 15!  22^  35 

Piston  displacement,  cubic  feet 2.71           5-53  I3-39 

Clearance,  per  cent      13  14  7 

Cut-off,  per  'cent  stroke 66  66  66 

Release,  per  cent  stroke 93  93  93 

Compression,  per  cent  stroke 18  18  18 

Ratio  of  piston  displacements i                  2 . 04  4-94 

Volume  first  receiver,  cubic  feet 2.22 

Volume  second  receiver,  cubic  feet 6.26 

Ratio  of  receiver  volumes  to  high-pressure  piston  dis- 
placement            0.82  2.31 

Stroke,  inches 24 

Boiler-pressure,  absolute,  pounds  per  sq.  in 180 

Pressure  in  condenser,  pounds  per  sq.  in 2 

If  the  volume  of  the  high-pressure  piston  displacement  is 
taken  to  be  unity,  then  the  volumes  required  in  the  equations  for 


TRIPLE    ENGINES 


177 


Fig-  47- 


calculating  pressures,  when  the  cranks  have  the  order  high- 
pressure,  low-pressure,  and  intermediate,  are  as  follows: 


vb  =  0.79  vt  =vx  =  0.29 

vc  =  vd  =  i. 06         vm  =  0.98 


0.35 


=    2.  02 


Ve  =   1. 10 

v/  =  1.13 

Vg   =   Vh   =   0.88 

i>i  =  0.31 

vk  =  va  =  0.13 


VH  —   V0     =    1.26  Va  =   Vp   =    2.72 


VP  -  1-63 

Vj  =   Vr  =   2.l8 

T;S  =  2.28 

^  =  2.33 

vu  =  v,  =  1.85 
^  =  0.63 


3.60 


1.23 


4.94 


iy8  COMPOUND   ENGINES 

The  required  pressures  are: 


Pa 

=  pb  = 

150        A  =  I^5 

& 

=  A 

= 

25.6 

PC 

=   112 

pn  =  60.0 

A 

=  S2 

•3 

Pd 

=  A  = 

76. 

5 

A  =  5°- 

5 

A 

=   22 

.1 

A 

=  pf  = 

67. 

5 

A  =  A 

= 

28 

•3 

A 

=  18 

•5 

Ps 

=  67.5 

A  =  A 

= 

25 

•3 

A 

=  />£ 

= 

5 

A 

=  76.9 

A  =  25- 

i 

A 

=  17, 

.6 

A 

=  A  = 

73- 

5 

^>u  =  29. 

0 

Pi 

=  Pm  = 

69 

•3 

A  =  A 

=  28.2 

Diagrams  with  the  volumes  and  pressures  corresponding  to 
this  example  are  plotted  in  Fig.  46  with  convenient  vertical 
scales.  Actual  indicator-diagrams  taken  from  the  engine  are 
given  by  Fig.  47.  The  events  of  the  stroke  come  at  slightly 
different  piston  positions  on  account  of  the  irregularity  due  to 
the  connecting-rod,  and  the  drops  and  other  fluctuations  of 
pressure  are  gradual  instead  of  sudden;  moreover,  there  is  con- 
siderable loss  of  pressure  from  the  boiler  to  the  engine,  from  one 
cylinder  to  another,  and  from  the  low-pressure  cylinder  to  the 
condenser.  Nevertheless  the  general  forms  of  the  diagrams  are 
easily  recognized,  and  all  apparent  erratic  variations  are 
accounted  for. 

Designing  Compound  Engines.  —  The  designer  of  compound  ' 
and  multiple-expansion  engines  should  have  at  hand  a  well- 
systematized  fund  of  information  concerning  the  sizes,  pro- 
portions, and  powers  of  such  engines,  together  with  actual 
indicator-diagrams.  He  may  then,  by  a  more  or  less  direct 
method  of  interpolation  or  exterpolation,  assign  the  dimensions 
and  proportions  to  a  new  design,  and  can,  if  deemed  advisable, 
draw  or  determine  a  set  of  probable  indicator-diagrams  for  the 
new  engines.  If  the  new  design  differs  much  from  the  engines 
for  which  he  has  information,  he  may  determine  approximate 
diagrams  both  for  an  actual  engine  from  which  indicator-dia- 
grams are  at  hand,  and  for  the  new  design.  He  may  then 
sketch  diagrams  for  the  new  engine,  using  the  approximate 


DESIGNING    COMPOUND   ENGINES 


179 


diagrams  as  a  basis  and  taking  a  comparison  of  the  approximate 
and  actual  diagrams  from  the  engine  already  built,  as  a  guide. 
It  is  convenient  to  prepare  and  use  a  table  showing  the  ratios  of 
actual  mean  effective  pressures  and  approximate  mean  effective 
pressures.  Such  a  table  enables  the  designer  to  assign  mean 
effective  pressures  to  a  cylinder  of  the  new  engine  and  to  infer 
very  closely  what  its  horse-power  will  be.  It  is  also  very  useful 
as  a  check  in  sketching  probable  diagrams  for  a  new  engine, 
which  diagrams  are  not  only  useful  in  estimating  the  power  of  the 
new  engine,  but  in  calculating  stresses  on  the  members  of  that 
engine. 

A  rough  approximation  of  the  power  of  an  engine  may  be 
made  by  calculating  the  power  as  though  the  total  or  equivalent 
expansion  took  place  in  the  low-pressure  cylinder,  neglecting 
clearance  and  compression.  The  power  thus  found  is  to  be 
affected  by  a  factor  which  according  to  the  size  and  type  of  the 
engine  may  vary  from  0.6  to  0.9  for  compound  engines  and  from 
0.5  to  0.8  for  triple  engines.  Seaton  and  Rounthwaite  *  give  the 
following  table  of  multipliers  for  compound  marine  engines: 


MULTIPLIERS   FOR   FINDING    PROBABLE   M.E.P.    COMPOUND 
AND    TRIPLE   MARINE   ENGINES. 


Description  of  Engine. 

Jacketed. 

Un  jacketed. 

Receiver-compound,  screw-engines  . 

o  67  to  o  73 

o  58  to  o  68 

Receiver-compound,  paddle-engines     
Direct  expansion                   .        .                    . 

0.55  to  0.65 

O    71  to  O    7? 

Three-cylinder  triple,  merchant  ships  . 

o  64  to  o  68 

o  60  to  o  66 

Three-cylinder  triple,  naval  vessels  

o.zz  to  o.  6< 

Three-cylinder  triple,  gunboats  and  torpedo-boats 

o  60  to  o  67 

For  example,  let  the  boiler-pressure  be  80  pounds  by  the  gauge, 
or  94.7  pounds  absolute;  let  the  back- pressure  be  4  pounds 
absolute;  and  let  the  total  number  of  expansions  be  six,  so  that 
the  volume  of  steam  exhausted  to  the  condenser  is  six  times  the 


*  Pocket  Book  of  Marine  Engineering. 


COMPOUND    ENGINES 

volume  admitted  from  the  boiler.     Neglecting  the  effect  of  clear- 
ance and  compression,  the  mean  effective  pressure  is 

94.7  X  *  +  94-7  X  i  loge   f  -  4  X  i  =  40.06  =  M.E.P. 

If  the  large  cylinder  is  30  inches  in  diameter,  and  the  stroke 
is  4  feet,  the  horse-power  at  60  revolutions  per  minute  is 

^-2°-  X  40.06  X  2  X  4  X  60  -j-  33000  =  412  H.P. 


If  the  factor  to  be  used  in  this  case  is  0.75,  then  the  actual 
horse-power  will  be  about 

0.75  X  4°°  =  3°°  H.P. 

Binary  Engines.  —  Another  form  of  compound  engines  using 
two  fluids  like  steam  and  ether,  was  proposed  by  du  Trembly  *  in 
1850,  to  extend  the  lower  range  of  temperature  of  vapor-engines. 
At  that  time  the  common  steam-pressure  was  not  far  from  thirty 
pounds  by  the  gauge,  corresponding  to  a  temperature  of  250°  F. 
If  the  back-pressure  of  the  engine  be  assumed  to  be  1.5  pounds 
absolute  (115°?.),  the  efficiency  for  Carnot's  cycle  would  be 
approximately 

2150  —  115 

J  -  *  =  o.io. 

250  +  460 

If,  however,  by  the  use  of  a  more  volatile  fluid  the  result  at 
lower  temperature  could  be  reduced  to  65°  F.,  the  efficiency 
could  be  increased  to 

250  —  65 
-*—.  —  f-  =  0.26. 

250  -j-  460 

At  the  present  time  when  higher  steam-pressures  are  common, 
the  comparison  is  less  favorable.  Thus  the  temperature  of 
steam  at  150  pounds  by  the  gauge  is  365°  F.,  so  that  with  1.5 

*  Manuel  du  Conducteur  des  Machines  a  Vaporous  combinees  au  Machines 
Binaires,  also  Rankine  Steam  Engine,  p.  444. 


BINARY   ENGINES  l8l 

pounds  absolute  (or  115°  F.)  for  the  back-  pressure  the  efficiency 
for  Carnot's  cycle  is 

365  —  115 

365  +  460  = 

and  for  a  resultant  temperature  of  65°  F.,  the  efficiency  would  be 

36  -  65 


365 


If  a  like  gain  of  economy  could  be  obtained  in  practice,  it 
would  represent  a  saving  of  17  per  cent,  which  would  be  well 
worth  while.  Further  discussion  of  this  matter  of  economy  will 
be  given  in  Chapter  XI,  in  connection  with  experiments  on 
binary  engines  using  steam  and  sulphur-dioxide. 

The  practical  arrangement  of  a  binary  engine  substitutes  for 
the  condenser  an  appliance  having  somewhat  the  same  form  as 
a  tubular  surface-condenser,  the  steam  being  condensed  on  the 
outside  of  the  tubes  and  withdrawn  in  the  form  of  water  of  con- 
densation at  the  bottom.  Through  the  tubes  is  forced  the 
more  volatile  fluid,  which  is  vaporized  much  as  it  would  be  in  a 
"water-tube"  boiler.  The  vapor  is  then  used  in  a  cylinder 
differing  in  no  essential  from  that  for  a  steam-engine,  and  in  turn 
is  condensed  in  a  surface-condenser  which  is  cooled  with  water 
at  the  lowest  possible  temperature. 

An  ideal  arrangement  for  a  binary  engine  avoiding  the  use  of 
air-pumps  would  appear  to  be  the  combination  of  a  compound 
non-condensing  steam-engine  with  a  third  cylinder  on  the  binary 
system  which  should  have  for  its  working  substance  a  fluid  that 
would  give  a  convenient  pressure  at  2i2°F.,  and  a  pressure 
somewhat  above  the  atmosphere  at  60°  F.  There  is  no  known 
fluid  that  gives  both  these  conditions;  thus  ether  at  212°  F.  gives 
a  pressure  of  about  96  pounds  absolute,  but  its  boiling-point  at 
atmospheric  pressure  is  94°  F.,  consequently  it  would  from 
necessity  require  a  vacuum  and  an  air-pump  unless  the  ether 
could  be  entirely  freed  from  air,  and  leakage  into  the  vacuum 
space  entirely  prevented.  Sulphur-dioxide  gives  a  pressure  of  41 


182  COMPOUND    ENGINES 

pounds  absolute  at  60°  F.,  so  that  it  can  always  be  worked  at  a 
pressure  above  the  atmosphere;  but  212°  F.  would  give  an  incon- 
venient pressure,  and  in  practice  it  has  been  found  convenient 
to  run  the  steam-engine  with  a  vacuum  of  22  inches  of  mercury 
or  about  4  pounds  absolute,  which  gives  a  temperature  of  155°  F., 
at  which  sulphur-dioxide  has  a  pressure  of  1 80  pounds  per  square 
inch  by  the  gauge. 

The  attempt  of  du  Trembly  to  use  ether  for  the  second  fluid 
in  a  binary  engine  did  not  result  favorably,  as  his  fuel-con- 
sumption was  not  less  than  that  of  good  engines  of  that  time, 
which  appears  to  indicate  that  he  could  not  secure  favorable 
conditions. 


CHAPTER   X. 

TESTING  STEAM-ENGINES. 

THE  principal  object  of  tests  of  steam-engines  is  to  determine 
the  cost  of  power.  Series  of  engine  tests  are  made  to 
determine  the  effect  of  certain  conditions,  such  as  superheating 
and  steam-jackets,  on  the  economy  of  the  engine.  Again,  tests 
may  be  made  to  investigate  the  interchanges  of  heat  between  the 
steam  and  the  walls  of  the  cylinder  by  the  aid  of  Hirn's  analysis, 
and  thus  find  how  certain  conditions  produce  effects  that  are 
favorable  or  unfavorable  to  economy. 

The  two  main  elements  of  an  engine  test  are,  then,  the  meas- 
urement of  the  power  developed  and  the  determination  of  the 
cost  of  the  power  in  terms  of  thermal  units,  pounds  of  steam,  or 
pounds  of  coal.  Power  is  most  commonly  measured  by  aid  of 
the  steam-engine  indicator,  but  the  power  delivered  by  the 
engine  is  sometimes  determined  by  a  dynamometer  or  a  friction 
brake;  sometimes,  when  an  indicator  cannot  be  used  conven- 
iently, the  dynamic  or  brake  power  only  is  determined.  When 
the  engine  drives  a  dynamo-electric  generator  the  power  applied 
to  the  generator  may  be  determined  electrically,  and  thus  the 
power  delivered  by  the  engine  may  be  known. 

When  the  cost  of  power  is  given  in  terms  of  coal  per  horse- 
power per  hour,  it  is  sufficient  to  weigh  the  coal  for  a  definite 
period  of  time.  In  such  case  a  combined  boiler  and  engine  test 
is  made,  and  all  the  methods  and  precautions  for  a  careful  boiler 
test  must  be  observed.  The  time  required  for  such  a  test 
depends  on  the  depth  of  the  fire  on  the  grate  and  the  rate  of 
combustion.  For  factory  boilers  the  test  should  be  twenty-four 
hours  long  if  exact  results  are  desired. 

When  the  cost  of  power  is  stated  in  terms  of  steam  per  horse- 
power per  hour,  one  of  two  methods  may  be  followed.  When 

183 


184  TESTING  STEAM-ENGINES 

the  engine  has  a  surface-condenser  the  steam  exhausted  from  the 
engine  is  condensed,  collected,  and  weighed.  One  hour  is 
usually  sufficient  for  tests  under  favorable  conditions;  shorter 
intervals,  ten  or  fifteen  minutes,  give  fairly  uniform  results. 
The  chief  objection  to  this  method  is  that  the  condenser  is  liable 
to  leak  water  at  the  tube  packings.  Under  favorable  conditions 
the  results  of  tests  by  this  method  and  by  determining  the  feed- 
water  supplied  to  the  boiler  are  substantially  the  same.  In  tests 
on  non-condensing  and  on  jet-condensing  engines  the  steam- 
consumption  is  determined  by  weighing  or  measuring  the  feed- 
water  supplied  to  the  boiler  or  boilers  that  furnish  steam  to  the 
engine.  Steam  used  for  any  other  purpose  than  running  the 
engine,  for  example,  for  pumping,  heating,  or  making  determi- 
nations of  the  quality  of  the  steam,  must  be  determined  and 
allowed  for.  The  most  satisfactory  way  is  to  condense  and 
weigh  such  steam;  but  small  quantities,  as  for  determining 
quality  by  a  steam  calorimeter,  may  be  gauged  by  allowing  it  to 
flow  through  an  orifice.  Tests  which  depend  on  measuring  the 
feed- water  should  be  long  enough  to  minimize  the  effect  of  the 
uncertainty  of  the  amount  of  water  in  a  boiler  corresponding  to 
an  apparent  height  of  water  in  a  water-gauge;  for  the  apparent 
height  of  the  water-level  depends  largely  on  the  rate  of  vaporiza- 
tion and  the  activity  of  convection  currents. 

When  the  cost  of  power  is  expressed  in  thermal  units  it  is 
necessary  to  measure  the  steam-pressure,  the  amount  of  moisture 
in  the  steam  supplied  to  the  cylinder,  and  the  temperature  of  the 
condensed  steam  when  it  leaves  the  condenser.  If  steam  is  used 
in  jackets  or  reheaters  it  must  be  accounted  for  separately. 
But  it  is  customary  in  all  engine  tests  to  take  pressures  and 
temperatures,  so  that  the  cost  may  usually  be  calculated  in 
thermal  units,  even  when  the  experimenter  is  content  to  state  it 
in  pounds  of  steam. 

For  a  Hirn's  analysis  it  is  necessary  to  weigh  or  measure  the 
condensing  water,  and  to  determine  the  temperatures  at  admis- 
sion to  and  exit  from  the  condenser. 

Important  engines,  with  their  boilers  and  other  appurtenances, 


TESTING  STEAM-ENGINES 


are  commonly  built  under  contract  to  give  a  certain  economy, 
and  the  fulfilment  of  the  terms  of  a  contract  is  determined  by  a 
test  of  the  engine  or  of  the  whole  plant.  The  test  of  the  entire 
plant  has  the  advantage  that  it  gives,  as  one  result,  the  cost  of 
power  directly  in  coal ;  but  as  the  engine  is  often  watched  with  more 
care  during  a  test  than  in  regular  service,  and  as  auxiliary  duties, 
such  as  heating  and  banking  fires,  are  frequently  omitted  from 
such  an  economy  test,  the  actual  cost  of  power  can  be  more 
justly  obtained  from  a  record  of  the  engine  in  regular  service, 
extending  for  weeks  or  months.  The  tests  of  engine  and  boilers, 
though  made  at  the  same  time,  need  not  start  and  stop  at  the 
same  time,  though  there  is  a  satisfaction  in  making  them 
strictly  simultaneous.  This  requires  that  the  tests  shall  be  long 
enough  to  avoid  drawing  the  fires  at  beginning  and  end  of  the 
boiler  test. 

In  anticipation  of  a  test  on  an  engine  it  must  be  run  for  some 
time  under  the  conditions  of  the  test,  to  eliminate  the  effects  of 
starting  or  of  changes.  Thus  engines  with  steam-jackets  are 
commonly  started  with  steam  in  the  jackets,  even  if  they  are  to 
run  with  steam  excluded  from  the  jackets.  An  hour  or  more 
must  then  be  allowed  before  the  effect  of  using  steam  in  the 
jackets  will  entirely  pass  away.  An  engine  without  steam- 
jackets,  or  with  steam  in  the  jackets,  may  come  to  constant 
conditions  in  a  fraction  of  that  time,  but  it  is  usually  well  to 
allow  at  least  an  hour  before  starting  the  test. 

It  is  of  the  first  importance  that  all  the  conditions  of  a  test 
shall  remain  constant  throughout  the  test.  Changes  of  steam- 
pressure  are  particularly  bad,  for  when  the  steam-pressure  rises 
the  temperature  of  the  engine  and  all  parts  affected  by  the  steam 
must  be  increased,  and  the  heat  required  for  this  purpose  is 
charged  against  the  performance  of  the  engine;  if  the  steam- 
pressure  falls  a  contrary  effect  will  be  felt.  In  a  series  of  tests 
one  element  at  a  time  should  be  changed,  so  that  the  effect  of 
that  element  may  not  be  confused  by  other  changes,  even  though 
such  changes  have  a  relatively  small  effect.  It  is,  however,  of 
more  importance  that  steam-pressure  should  remain  constant 


1 86  TESTING    STEAM-ENGINES 

than  that  all  tests  at  a  given  pressure  should  have  identically  the 
same  steam- pressure,  because  the  total  heat  of  steam  varies  more 
slowly  than  the  temperature. 

All  the  instruments  and  apparatus  used  for  an  engine  test 
should  be  tested  and  standardized  either  just  before  or  just 
after  the  test;  preferably  before,  to  avoid  annoyance  when  any 
instrument  fails  during  the  test  and  is  replaced  by  another. 

Thermometers.  —  Temperatures  are  commonly  measured  by 
aid  of  mercurial  thermometers,  of  which  three  grades  may  be 
distinguished.  For  work  resembling  that  done  by  the  physicist 
the  highest  grade  should  be  used,  and  these  must  ordinarily  be 
calibrated,  and  have  their  boiling-  and  freezing-points  deter- 
mined by  the  experimenter  or  some  qualified  person;  since  the 
freezing-point  is  liable  to  change,  it  should  be  redetermined  when 
necessary.  For  important  data  good  thermometers  must  be  used, 
such  as  are  sold  by  reliable  dealers,  but  it  is  preferable  that  they 
should  be  calibrated  or  else  compared  with  a  thermometer  that 
is  known  to  be  reliable.  For  secondary  data  or  for  those  requir- 
ing little  accuracy  common  thermometers  with  the  graduation 
on  the  stem  may  be  used,  but  these  also  should  have  their  errors 
determined  and  allowed  for.  Thermometers  with  detachable 
scales  should  be  used  only  for  crude  work. 

Gauges.  —  Pressures  are  commonly  measured  by  Bourdon 
gauges,  and  if  recently  compared  with  a  correct  mercury  column 
these  are  sufficient  for  engineering  work.  The  columns  used 
by  gauge-makers  are  sometimes  subject  to  minor  errors,  and  are 
not  usually  corrected  for  temperature.  It-  is  important  that 
such  gauges  should  be  frequently  retested. 

Dynamometers.  —  The  standard  for  measurement  of  power 
is  the  friction-brake.  For  smooth  continuous  running  it  is 
essential  that  the  brake  and  its  band  shall  be  cooled  by  a  stream 
of  water  that  does  not  come  in  contact  with  the  rubbing  sur- 
faces. Sometimes  the  wheel  is  cooled  by  a  stream  of  water  cir- 
culating through  it,  sometimes  the  band  is  so  cooled,  or  both  may 
be.  A  rubbing  surface  which  is  not  cooled  should  be  of  non- 
conducting material.  If  both  rubbing  surfaces  are  metallic  they 


INDICATORS  igy 

must  be  freely  lubricated  with  oil.  An  iron  wheel  running  in  a 
band  furnished  with  blocks  of  wood  requires  little  or  no  lubri- 
cation. 

To  avoid  the  increase  of  friction  on  the  brake- bearings  due 
to  the  load  applied  at  a  single  brake-arm,  two  equal  arms  may 
be  used  with  two  equal  and  opposite  forces  applied  at  the  ends 
to  form  a  statical  couple. 

With  care  and  good  workmanship  a  friction-brake  may  be 
made  an  instrument  of  precision  sufficient  for  physical  investi- 
gations, but  with  ordinary  care  and  workmanship  it  will  give 
results  of  sufficient  accuracy  for  engineering  work. 

An  engine  which  drives  an  electric-generator  may  readily  have 
the  dynamic  or  brake-power  determined  from  the  electric  out- 
put, provided  that  the  efficiency  of  the  generator  is  properly 
determined. 

The  only  power  that  can  be  measured  for  a  steam-turbine  is 
the  dynamic  or  brake-power;  when  connected  with  an  electric- 
generator  this  involves  no  difficulty.  For  marine  propulsion  it 
is  customary  to  determine  the  power  of  steam-turbines  by  some 
form  of  torsion-metre  applied  to  the  shaft  that  connects  the 
turbine  to  the  propeller.  This  instrument  measures  the  angle 
of  torsion  of  the  shaft  while  running,  and  consequently,  if  the 
modulus  of  elasticity  has  been  determined,  gives  a  positive 
determination  of  the  power  delivered  to  the  propeller.  Under 
favorable  conditions  a  torsion-metre  may  have  an  error  of  not 
more  than  one  per  cent. 

Indicators.  —  The  most  important  and  at  the  same  time  the 
least  satisfactory  instrument  used  in  engine-testing  is  the  indi- 
cator. Even  when  well  made  and  in  good  condition  it  is  liable 
to  have  an  error  which  may  amount  to  two  per  cent  when  used 
at  moderate  speeds.  At  high  speeds,  three  hundred  revolutions 
per  minute  and  over,  it  is  likely  to  have  two  or  three  times  as 
much  error.  As  a  rule,  an  indicator  cannot  be  used  at  more 
than  four  hundred  revolutions  per  minute. 

The  mechanism  for  reducing  the  motion  of  the  crosshead  of 
the  engine  and  transferring  it  to  the  paper  drum  of  an  indicator 


1 88  TESTING    STEAM-ENGINES 

should  be  correct  in  design  and  free  from  undue  looseness.  It 
should  require  only  a  very  short  cord  leading  to  the  paper  drum, 
because  all  the  errors  due  to  the  paper  drum  are  proportional  to 
the  length  of  the  cord  and  may  be  practically  eliminated  by 
making  the  cord  short. 

The  weighing  and  recording  of  the  steam-pressure  by  the  indi- 
cator-piston, pencil-motion,  and  pencil  are  affected  by  errors 
which  may  be  classified  as  follows : 

1.  Scale  of  the  spring. 

2.  Design  of  the  pencil-motion. 

3.  Inertia  of  moving  parts. 

4.  Friction  and  backlash. 

Good  indicator-springs,  when  tested  by  direct  loads  out  of 
the  indicator,  usually  have  correct  and  uniform  scales;  that  is, 
they  collapse  under  pressure  the  proper  amount  for  each  load 
applied.  When  enclosed  in  the  cylinder  of  an  indicator  the 
spring  is  heated  by  conduction  and  radiation  to  the  temperature 
of  the  cylinder,  and  that  temperature  is  sensibly  equal  to  the 
mean  temperature  in  the  engine-cylinder.  But  a  spring  is  appre- 
ciably weaker  at  high  temperatures,  so  that  when  thus  enclosed 
in  the  indicator-cylinder,  it  gives  results,  that  are  too  large;  the 
error  may  be  two  per  cent  or  more. 

Outside  spring-indicators  avoid  this  difficulty  and  are  to  be 
preferred  for  all  important  work.  They  have  only  one  disad- 
vantage, in  that  the  moving  parts  are  heavier,  but  this  may  be 
overcome  by  increasing  the  area  of  the  piston  from  half  a  square 
inch  to  one  square  inch. 

The  motion  of  the  piston  of  the  indicator  is  multiplied  five 
or  six  times  by  the  pencil-motion,  which  is  usually  an  approx- 
imate parallel  motion.  Within  the  proper  range  of  motion 
(about  two  inches)  the  pencil  draws  a  line  which  is  nearly 
straight  when  the  paper  drum  is  at  rest,  and  it  gives  a  nearly 
uniform  scale  provided  that  the  spring  is  uniform.  The  errors 
due  to  the  geometric  design  of  this  part  of  the  indicator  are 
always  small. 


INDICATORS  189 

When  steam  is  suddenly  let  into  the  indicator,  as  at  admission 
to  the  engine-cylinder,  the  indicator-piston  and  attached  parts 
forming  the  pencil-motion  are  set  into  vibration,  with  a  natural 
time  of  vibration  depending  on  the  stiffness  of  the  spring.  A 
weak  spring  used  for  indicating  a  high-speed  engine  may  throw 
the  diagram  into  confusion,  because  the  pencil  will  give  a  few 
deep  undulations  which  make  it  impossible  to  recognize  the 
events  of  the  stroke  of  the  engine,  such  as  cut-off  and  release. 
A  stiffer  spring  will  give  more  rapid  and  less  extensive  undu- 
lations, which  will  be  much  less  troublesome.  As  a  rule,  when 
the  undulations  do  not  confuse  the  diagram  the  area  of  the  dia- 
gram is  but  little  affected  by  the  undulations  due  to  the  inertia 
of  the  piston  and  pencil-motion. 

The  most  troublesome  errors  of  the  indicator  are  due 
to  friction  and  backlash.  The  various  joints  at  the  piston 
and  in  the  pencil-motion  are  made  as  tight  as  can  be  without 
undue  friction,  but  there  is  always  some  looseness  and  some 
friction  at  those  joints.  There  is  also  some  friction  of  the  piston 
in  the  cylinder  and  of  the  pencil  on  the  paper.  Errors  from  this 
source  may  be  one  or  two  per  cent,  and  are  liable  be  excessive 
unless  the  instrument  is  used  with  care  and  skill.  A  blunt 
pencil  pressed  up  hard  on  the  paper  will  reduce  the  area  of  the 
diagram  five  per  cent  or  more;  on  the  other  hand,  a  medium 
pencil  drawing  a  faint  but  legible  line  will  affect  the  area  very 
little.  Any  considerable  friction  of  the  piston  of  the  indicator 
will  destroy  the  value  of  the  diagram. 

Errors  of  the  scale  of  the  spring  can  be  readily  determined  and 
investigated  by  loading  the  spring  with  known  weights,  when 
properly  supported,  out  of  the  indicator.  This  method  is  prob- 
ably sufficient  for  outside  spring  indicators.  Those  that  have 
the  spring  inside  the  cylinder  are  tested  under  steam  pressure, 
measuring  the  pressure  either  by  a  gauge  or  a  mercury  column. 
Considerable  care  and  skill  are  required  to  get  good  results, 
especially  to  avoid  excessive  friction  of  the  piston  as  it  remains 
at  rest  or  moves  slowly  in  the  cylinder.  It  must  be  borne  in 
mind  that  the  indicator  cylinder  heats  readily  when  subjected  to 


I90  TESTING   STEAM-ENGINES 

progressively  higher  steam  pressures,  but  that  it  parts  with  heat 
slowly,  and  that  consequently  tests  made  with  falling  steam 
pressures  are  not  valuable. 

Scales.  —  Weighing  should  be  done  on  scales  adapted  to  the 
load;  overloading  leads  to  excessive  friction  at  the  knife-edges  and 
to  lack  of  delicacy.  Good  commercial  platform  scales,  when 
tested  with  standard  weights,  are  sufficient  for  engineering  work. 

Coal  and  ashes  are  readily  weighed  in  barrows,  for  which  the 
tare  is  determined  by  weighing  empty.  Water  is  weighed  in 
barrels  or  tanks.  The  water  can  usually  be  pumped  in  or 
allowed  to  run  in  under  a  head,  so  that  the  barrel  or  tank  can  be 
filled  promptly.  Large  quick-opening  valves  must  be  used  to  allow 
the  water  to  run  out  quickly.  As  the  receptacle  will  seldom  drain 
properly,  it  is  not  well  to  wait  for  it  to  drain,  but  to  close  the 
exit- valve  and  weigh  empty  with  whatever  small  amount  of  water 
may  be  caught  in  it.  Neither  is  it  well  to  try  to  fill  the  receptacle 
to  a  given  weight,  as  the  jet  of  water  running  in  may  affect  the 
weighing.  With  large  enough  scales  and  tanks  the  largest 
amounts  of  water  used  for  engine  tests  may  be  readily  handled. 

Measuring  Water.  —  When  it  is  not  convenient  to  weigh  water 
directly,  it  may  be  measured  in  tanks  or  other  receptacles  of 
known  volume.  Commonly  two  are  used,  so  that  one  may 
fill  while  the  other  is  emptied.  The  volume  of  a  receptacle  may 
be  calculated  from  its  dimensions,  or  may  be  determined  by 
weighing  in  water  enough  to  fill  it.  When  desired  a  receptacle 
may  be  provided  with  a  scale  showing  the  depth  of  the  water, 
and  so  partial  volumes  can  be  determined.  A  closed  recep- 
tacle may  be  used  to  measure  hot  water  or  other  fluids. 

Water-Meters  of  good  make  may  be  used  for  measuring  water 
when  other  methods  are  not  applicable,  provided  they  are  tested 
and  rated  under  the  conditions  for  which  they  are  used,  taking 
account  of  the  amount  and  temperature  of  the  water  measured. 
Metres  are  most  convenient  for  testing  marine  engines  because 
water  cannot  be  weighed  at  sea  on  account  of  the  motion  of  the 
ship,  and  arrangements  for  measuring  water  in  tanks  are  expen- 
sive and  inconvenient.  For  such  tests  the  metre  may  be  placed 


THROTTLING-CALORIMETER  191 

on  a  by- pass  through  which  the  feed- water  from  the  surface- 
condenser  can  be  made  to  pass  by  closing  a  valve  on  the  direct 
line  of  feed-pipe.  If  necessary  the  metre  can  be  quickly  shut 
off  and  the  direct  line  can  be  opened.  The  chief  uncertainty  in 
the  use  of  a  metre  is  due  to  air  in  the  water;  to  avoid  error  from 
this  source,  the  metre  should  be  frequently  vented  to  allow  air 
to  escape  without  being  recorded  by  the  metre. 

Weirs  and  Orifices.  —  So  far  as  possible  the  use  of  weirs  and 
orifices  for  water  during  engine  tests  should  be  avoided,  for,  in 
addition  to  the  uncertainties  unavoidably  connected  with  such 
hydraulic  measurements,  difficulties  are  liable  to  arise  from  the 
temperature  of  the  water  and  from  the  oil  in  it.  A  very  little  oil 
is  enough  to  sensibly  affect  the  coefficient  for  a  weir  'or  orifice. 
The  water  flowing  from  the  hot-well  of  a  jet-condensing  engine 
is  so  large  in  amount  that  it  is  usually  deemed  advisable  to 
measure  it  on  a  weir;  the  effect  of  temperature  and  oil  is  less 
than  when  the  same  method  is  used  for  measuring  condensed 
steam  from  a  surface-condenser. 

Priming-Gauges.  —  When  superheated  steam  is  supplied  to  an 
engine  it  is  sufficient  to  take  the  temperature  of  the  steam  in  the 
steam-pipe  near  the  engine.  When  moist  steam  is  used  the  amount 
of  moisture  must  be  determined  by  a  separated  test.  Origi- 
nally such  tests  were  made  by  some  form  of  calorimeter,  and 
that  name  is  now  commonly  attached  to  certain  devices  which 
are  not  properly  heat-measurers.  Three  of  these  will  be  men- 
tioned :  (i )  the  throttling-calorimeter,  which  can  usually  be  applied 
to  all  engine  tests;  (2)  the  separating-calorimeter,  which  can  be 
applied  when  the  steam  is  wet;  and  (3)  the  Thomas  electric  calor- 
imeter, intended  for  use  with  steam-turbines  to  determine  the 
moisture  in  steam  at  any  stage  of  the  turbine  whatever  may  be 
the  pressure  or  quality  of  the  steam. 

Throttling-Calorimeter.  —  A  simple  form  of  calorimeter, 
devised  by  the  author,  is  shown  by  Fig.  48,  where  A  is  a 
reservoir  about  4  inches  in  diameter  and  about  12  inches  long 
to  which  steam  is  admitted  through  a  half-inch  pipe  b,  with  a 
throttle-valve  near  the  reservoir.  Steam  flows  away  through  an 


192 


TESTING    STEAM-ENGINES 


inch  pipe  d.  At  /  is  a  gauge  for  measuring  the  pressure,  and  at 
e  there  is  a  deep  cup  for  a  thermometer  to  measure  the  temper- 
ature. The  boiler-pressure  may  be  taken 
from  a  gauge  on  the  main  steam-pipe 
near  the  calorimeter.  It  should  not  be 
taken  from  a  pipe  in  which  there  is  a 
rapid  flow  of  steam  as  in  the  pipe  b, 
since  the  velocity  of  the  steam  will  affect 
the  gauge-reading,  making  it  less  than  the 
real  pressure.  The  reservoir  is  wrapped 
with  hair-felt  and  lagged  with  wood  to 
reduce  radiation  of  heat. 

When  a  test  is  to  be  made,  the  valve  on 
the  pipe  d  is  opened  wide  (this  valve  is 
frequently  omitted),  and  the  valve  at  b  is 
opened  wide  enough  to  give  a  pressure  of 
five  to  fifteen  pounds  in  the  reservoir. 
Readings  are  then  taken  of  the  boiler- 
gauge,  of  the  gauge  at  /,  and  of  the  thermometer  at  e.  It  is  well  to 
wait  about  ten  minutes  after  the  instrument  is  started  before  taking 
readings  so  that  it  may  be  well  heated.  Let  the  boiler-pressure 
be  p,  and  let  r  and  q  be  the  latent  heat  and  heat  of  the  liquid 
corresponding.  Let  pl  be  the  pressure  in  the  calorimeter,  rl  the 
heat  of  vaporization,  qt  the  heat  of  the  liquid,  and  tl  the  tempera- 
ture of  saturated  steam  at  that  pressure,  while  ls  is  the  tempera- 
ture of  the  superheated  steam  in  the  calorimeter.  Then 

xr  +  q  =  rl  +  ql  +  cp  (/.  —  /J; 

r.  +  ql  +  cv  (ts  -  Q  -  ? 


FIG.  48. 


Example.  —  The  following  are  the  data  of  a  test  made  with 
this  calorimeter: 

Pressure  of  the  atmosphere  ....      14.8  pounds; 
Steam- pressure  by  gauge      ....      69.8 
Pressure  in  the  calorimeter,  gauge      .      12,0 
Temperature  in  the  calorimeter     .     .  268°. 2  F. 


THROTTLING-CALORIMETER 


193 


Specific  heat  of  superheated  steam  for  the  condition  of  the 
test  0.46 

948.8  +  212.6  +  0.46  (268.2)  -  243.9)   — 

896.8 

Per  cent  of  priming,  1.2. 


-  =o.988; 


A  little  consideration  shows  that  this  type  of  calorimeter 
can  be  used  only  when  the  priming  is  not  excessive;  otherwise 
the^  throttling  will  fail  to  superheat  the  steam,  and  in  such  case 
nothing  can  be  told  about  the  condition  of  the  steam  either  before 
or  after  throttling.  To  find  this  limit  for  any  pressure  tt  may  be 
made  equal  to  ^  in  equation (152);  that  is,  we  may  assume  that 
the  steam  is  just  dry  and  saturated  at  that  limit  in  the  calorimeter. 
Ordinarily  the  lowest  convenient  pressure  in  the  calorimeter  is 
the  pressure  of  the  atmosphere,  or  14.7  pounds  to  the  square  inch. 
The  table  following  has  been  calculated  for  several  pressures  in 
the  manner  indicated.  It  shows  that  the  limit  is  higher  for  higher 
pressures,  but  that  the  calorimeter  can  be  applied  only  where 
the  priming  is  moderate. 

When  this  calorimeter  is  used  to  test  steam  supplied  to  a 
condensing-engine  the  limit  may  be  extended  by  connecting  the 
exhaust  to  the  condenser.  For  example,  the  limit  at  100  pounds 
absolute,  with  3  pounds  absolute  in  the  calorimeter,  is  0.064 
instead  of  0.040  with  atmospheric  pressure  in  the  calorimeter. 

LIMITS    OF   THE   THROTTLING-CALORIMETER. 


Pressure. 

Priming. 

Absolute. 

Gauge. 

300 

285.3 

0.077 

250 

235-3 

0.070 

2OO 

l85.3 

0.061 

I7S 

160.3 

0.058 

150 

135-3 

0.052 

I25 

110.3 

0.046 

100 

85-3 

0.040 

75 

60.3 

0.032 

So 

35-3 

o  ,  023 

IQ4  TESTING   STEAM-ENGINES 

In  case  the  calorimeter  is  used  near  its  limit  —  that  is,  when 
the  superheating  is  a  few  degrees  only  —  it  is  essential  that  the 
thermometer  should  be  entirely  reliable;  otherwise  it  might 
happen  that  the  thermometer  should  show  superheating  when 
the  steam  in  the  calorimeter  was  saturated  or  moist.  In  any 
other  case  a  considerable  error  in  the  temperature  will  produce 
an  inconsiderable  effect  on  the  result.  Thus  at  100  pounds 
absolute  with  atmospheric  pressure  in  the  calorimeter,  10°  F.  of 
superheating  indicates  0.035  priming,  and  i5°F.  indicates  0.032 
priming.  So  also  a  slight  error  in  the  gauge-reading  has  little 
effect.  Suppose  the  reading  to  be  apparently  100.5  pounds 
absolute  instead  of  100,  then  with  10°  of  superheating  the  prim- 
ing appears  to  be  0.033  instead  of  0.032. 

It  has  been  found  by  experiment  that  no  allowance  need  be 
made  for  radiation  from  this  calorimeter  if  made  as  described, 
providecl  that  200  pounds  of  steam  are  run  through  it  per  hour. 
Now  this  quantity  will  flow  through  ag  orifice  one-fourth  of  an 
inch  in  diameter  under  the  pressure  of  70  pounds  by  the  gauge, 
so  that  if  the  throttle-valve  be  replaced  by  such  an  orifice  the 
question  of  radiation  need  not  be  considered.  In  such  case  a 
stop-valve  will  be  placed  on  the  pipe  to  shut  off  the  calorimeter 
when  not  in  use;  it  is  opened  wide  when  a  test  is  made.  If  an 
orifice  is  not  provided  the  throttle-valve  may  be  opened  at  first 
a  small  amount,  and  the  temperature  in  the  calorimeter  noted; 
after  a  few  minutes  the  valve  may  be  opened  a  trifle  more,  where- 
upon the  temperature  may  rise,  if  too  little  steam  was  used  at 
first.  If  the  valve  is  opened  little  by  little  till  the  temperature 
stops  rising,  it  will  then  be  certain  that  enough  steam  is  used  to 
reduce  the  error  from  radiation  to  a  very  small  amount. 

Separating-Calorimeter.  —  If  steam  contains  more  than 
three  per  cent  of  moisture  the  priming  may  be  determined  by 
a  good  separator  which  will  remove  nearly  all  the  moisture. 
It  remains  to  measure  the  steam  and  water  separately.  The 
water  may  be  best  measured  in  a  calibrated  vessel  or  receiver, 
while  the  steam  may  be  condensed  and  weighed,  or  may  be 
gauged  by  allowing  it  to  flow  through  an  orifice  of  known  size. 


THE   THOMAS    ELECTRIC    CALORIMETER 


A  form  of  separating-calorimeter  devised  by  Professor  Carpenter  * 
is  shown  by  Fig.  49. 

Steam  enters  a  space  at  the  top 
which  has  sides  of  wire  gauze  and  a 
convex  cup  at  the  bottom.  The  water 
is  thrown  against  the  cup  and  finds  its 
way  through  the  gauze  into  an  inside 
chamber  or  receiver  and  rises  in  a 
water-glass  outside.  The  receiver  is 
calibrated  by  trial,  so  that  the  amount  of 
water  may  be  read  directly  from  a  gradu- 
ated scale.  The  steam  meanwhile  passes 
into  the  outer  chamber  which  surrounds 
the  inner  receiver  and  escapes  from  an 
orifice  at  the  bottom.  The  steam  may 
be  determined  by  condensing,  collecting, 
and  weighing  it;  or  it  may  be  calculated 
from  the  pressure  and  the  size  of  the 
orifice.  When  the  steam  is  weighed 
there  is  no  radiation  error,  since  the 

inner  chamber  is  protected  by  the  steam  in  the  outer  chamber. 
This  instrument  may  be  guarded  against  radiation  by  wrapping 
and  lagging,  and  then  if  steam  enough  is  used  the  radiation  will 
be  insignificant,  just  as  was  found  to  be  the  case  for  the 
throttling-calorimeter. 

The  Thomas  Electric  Calorimeter. — The  essential  feature  of  this 
instrument  (Fig.  50)  is  the  drying  and  superheating  of  the  steam 
by  a  measured  amount  of  electric  energy.  Steam  is  admitted 
at  B  and  passes  through  numerous  holes  in  a  block  of  soapstone 
which  occupies  the  middle  of  the  instrument;  these  holes  are 
partially  filled  with  coils  of  German  silver  wire  which  are  heated 
by  an  electric  current  that  enters  and  leaves  at  the  binding- 
screws.  The  steam  emerges  dry  or  superheated  at  the  upper 
part  of  the  chamber  and  passes  down  through  wire  gauze,  which 
surrounds  the  central  escape  pipe;  this  central  pipe  surrounds 

*  Trans.  Am.  Soc.  Mech.  Engs.,  vol.  xvii,  p.  608. 


FIG.  49- 


TESTING   STEAM-ENGINES 


the  thermometer  cup,  and  leads  to  the  exit  at  the  top,  which  has 
two  orifices,  either  of  which  may  be  piped  to  a  condenser  or 

elsewhere. 

To  use  the  instrument  it  is 
properly  connected  by  a  sampling- 
tube  to  the  space  from  which 
steam  is  drawn,  and  valves  are 
adjusted  to  supply  a  convenient 
amount  of  steam  which  is  assumed 
to  be  uniform  for  steady  pressure; 
this  last  is  a  matter  of  some  im- 
portance. 

The  current  of  electricity  is 
then  adjusted  to  dry  the  steam; 
this  may  be  determined  by  noting 
the  temperature  by  the  thermom- 
eter in  the  central  thermometer 
cup,  because  that  thermometer 
will  show  a  slight  rise  corres- 
ponding to  a  very  small  degree 
of  superheating  which  is  sufficient 
to  indicate  the  disappearance  of 
moisture,  but  not  enough  to  affect 
the  determination  of  quality  by 
the  instrument.  The  wire  gauze 
surrounding  the  thermometer  is  an  essential  feature  of  this 
operation,  as  it  insures  the  homogeneity  of  the  steam,  which, 
without  the  gauze,  would  be  likely  to  be  a  mixture  of  super- 
heated steam  and  moist  steam.  Readings  are  taken  of  the 
proper  electrical  instruments  from  which  the  electrical  energy 
imparted  can  be  determined  in  watts;  let  this  energy  required  to 
dry  the  steam  be  denoted  by  Ev  Now  let  the  electric  current  be 
increased  till  the  steam  is  superheated  30°,  and  let  E2  be  the 
increase  of  electric  input  which  is  required  to  superheat  the 
steam. 

If  W  is  the  weight  of  steam  flowing  per  hour  through  the 


FIG.  50. 


THE   THOMAS   ELECTRIC    CALORIMETER  197 

instrument  under  the  first  conditions,  the  weight  when  super- 
heated will  be  CW,  where  C  is  a  factor  less  than  unity  which 
has  been  determined  by  exhaustive  tests  on  the  instrument. 
The  amount  of  electric  energy  required  to  superheat  one  pound 
of  steam  30°  from  saturation  at  various  pressures  has  also  been 
determined  and  may  be  represented  by  S;  this  constant  has  been 
so  determined  as  to  include  an  allowance  for  radiation,  and  is 
more  convenient  than  the  specific  heat  of  superheated  steam,  in 
this  place.  Making  use  of  the  factors  C  and  5,  we  may  write 

E2  =  CSW,  orW  =  J£, 

which  affords  a  means  of  eliminating  the  weight  of  steam  used; 
this  is  an  important  feature  in  the  use  of  the  instrument. 

Returning  now  to  the  first  condition  of  the  instrument  when 
steam  is  dried  by  the  application  of  E^  watts  of  electric  energy, 
we  have  for  the  equivalent  heat 

3-42  Ej 

and  dividing  by  the  expression  for  the  weight  of  steam  flowing 
per  hour,  we  have  for  the  heat  required  to  dry  one  pound  of 
steam 

7.42  E.  ^0    E*        ,  N 

W       =^2CS   £"(i-*)', 

where  r  is  the  heat  of  vaporization  and  i  —  x  is  the  amount  of 
water  in  one  pound  of  moist  steam. 

Solving  the  above  equation  for  xt  we  have 

,.,-aiSi. 

If  desired,  the  constant  factors  may  be  united  into  one  term,  and 
the  equation  may  be  written 

K  E 


With  each  instrument  is  furnished  a  diagram  giving  values  of 
K  for  all  pressures,  so  that  the  use  of  the  instrument  involves 


198  TESTING    STEAM-ENGINES 

only  two  readings  of  a  wattmeter  and  the  application  of  the  above 
simple  equation. 

For  example,  suppose  that  the  use  of  the  instrument  in  a 
particular  case  gave  the  values  El  =  240,  and  E2  =  93.0  for 
the  absolute  pressure  100  pounds  per  square  inch.  The  value 
of  K  from  the  diagram  is  54.2,  and  r  from  the  steam-  tables  is  884, 
consequently 


.     240 
x  =  i  —  —  --  —  =  0.84. 

884  93.0 

Method  of  Sampling  Steam.  —  It  is  customary  to  take  a  sample 
of  steam  .for  a  calorimeter  or  priming-gauge  through  a  small 
pipe  leading  from  the  main  steam-pipe.  The  best  method  of 
securing  a  sample  is  an  open  question;  indeed,  it  is  a  question 
whether  we  ever  get  a  fair  sample.  There  is  no  question  but 
that  the  composition  of  the  sample  is  correctly  shown  by  any  of 
the  calorimeters  described,  when  the  observer  makes  tests  with 
proper  care  and  skill.  It  is  probable  that  the  best  way  is  to 
take  steam  through  a  pipe  which  reaches  at  least  halfway  across 
the  main  steam-pipe,  and  which  is  closed  at  the  end  and  drilled 
full  of  small  holes.  It  is  better  to  have  the  sampling-pipe  at 
the  side  or  top  of  the  main,  and  it  is  better  to  take  a  sample 
from  a  pipe  through  which  steam  flows  vertically  upward.  The 
sampling-pipe  should  be  short  and  well  wrapped  to  avoid 
radiation. 


CHAPTER  XI. 

INFLUENCE   OF  THE   CYLINDER  WALLS. 

IN  this  chapter  a  discussion  will  be  given  of  the  discrepancy 
between  the  theory  of  the  steam-engine  as  detailed  in  the  previous 
chapter,  and  the  actual  performance  as  determined  by  tests  on 
engines.  It  was  early  evident  that  this  discrepancy  was  due 
to  the  interference  of  the  metal  of  the  cylinder  walls  which 
abstracted  heat  from  the  steam  at  high  pressure  and  gave  it  out 
at  low  pressure.  In  consequence  there  followed  a  long  struggle 
to  determine  precisely  what  action  the  walls  exerted  and  how  to 
allow  for  that  action  in  the  design  of  new  engines.  The  first 
part  has  been  accomplished ;  we  can  determine  to  a  nicety  the 
influence  of  the  cylinder  walls  for  any  engine  already  built  and 
tested;  but  as  yet  all  attempts  to  systematize  the  information 
derived  from  such  tests  in  such  a  manner  that  it  can  be  used 
in  the  design  of  new  engines  has  been  utterly  futile.  Conse- 
quently the  discussion  in  this  chapter  is  important  mainly 
in  that  it  allows  us  to  understand  the  real  action  of  certain 
devices  that  are  intended  to  improve  the  economy  of  engines, 
and  to  form  a  just  opinion  on  the  probability  of  future  im- 
provements. 

As  soon  as  the  investigations  by  Clausius  and  Rankine 
and  the  experiments  by  Regnault  made  a  precise  theory  of 
the  steam  engine  possible,  it  became  evident  that  engines  used 
from  quarter  to  half  again  as  much  steam  as  the  adiabatic 
theory  indicated,  and  in  particular  that  expansion  down  to 
the  back-pressure  was  inadvisable.  An  early  and  a  satis- 
factory exposition  of  these  points  was  made  by  Isherwood 
after  his  tests  on  the  U.  S.  S.  Michigan,  which  are  given  in 
Table  III. 


199 


200 


INFLUENCE    OF   THE    CYLINDER    WALLS 


TABLE    III. 

TESTS   ON   THE   ENGINE   OF   THE   U.  S.  S.  MICHIGAN. 

CYLINDER   DIAMETER,    36   INCHES;    STROKE,    8    FEET. 

By  Chief-Engineer  ISHERWOOD,  Researches  in  Experimental  Steam 
Engineering. 


I. 

II. 

III. 

IV. 

V. 

£ 

13-9 

21.  O 
29.9 
25.8 
34-5 

39-6 

VI. 

VII. 

Duration,  hours    

11/12 
20.6 

21.  O 
3O.I 
26.5 
38.0 
10.7 

72 

7/10 
iS-6 

19-5 
29.8 
26.1 

33-8 
15-3 

72 

4/9 
17-3 

21.0 
29.7 
26.3 

32-7 
27.2 

72 

3/10 
13-7 

21.  O 
3O.I 

25.8 

34-7 
41-7 

$ 

II.  2 

21.0 
29.9 
25.6 
36.8 
42.1 

4/45 
14-1 

22.0 
29.9 
24.1 
41.4 

45-i 

Cut-off  

Revolutions  per  minute  

Boiler-pressure,    pounds  per   sq   in.    above 
atmosphere    

Barometer,  inches  of  mercury    
Vacuum,  inches  of  mercury    
Steam  per  horse-power  per  hour,  pounds 
Per  cent  of  water  in  cylinder  at  release     .    . 

U.S.  S.  MICHIGAN 

Abscissae  per  cents  of  cut  off 
Ordinates  pounds  of  steam 
per  horse  power  per  hour. 


In  the  first  place  the  best  economy  for  this  engine  was  32.7 
pounds  instead  of  26.5  pounds  as  calculated  by  the  expression 

60  X  33000 

778  (r,  +  &  -  */2  -  &) 

deduced  on  page  141  for  the  steam-consumption  for  a  non-con- 
ducting engine  with 
complete  expansion. 
This  result  was  ob- 
tained with  cut-off  at 
four-ninths  of  the 
stroke  which  gave  a 
terminal  pressure  of 
one  pound  above  the 
atmosphere. 

The  manner  of  the 
variation  of  the  steam 
consumption  with  the 
cut-off  is  clearly 
shown  by  Fig.  51,  in 

which  the  fraction  of  stroke  at  cut-off  is  taken  for  abscissae  and 

the  steam-consumptions  as  ordinates. 


0.2 


0.1 


0.0 


0.8 


FIG.  51. 


INFLUENCE   OF   THE    CYLINDER   WALLS  2OI 

To  make  the  diagram  clear  and  compact,  the  axis  of  abscissae 
is  taken  at  30  pounds  of  steam  per  horse-power  per  hour.  An 
inspection  of  this  diagram  and  of  the  figures  in  the  table  shows 
a  regularity  in  the  results  which  can  be  attained  only  when  tests 
are  made  with  care  and  skill.  The  only  condition  purposely 
varied  is  the  cut-off;  the  only  condition  showing  important  acci- 
dental variation  is  the  vacuum,  and  consequently  the  back- 
pressure in  the  cylinder.  To  allow  for  the  small  variations  in 
the  back-pressure  Isherwood  changed  the  mean  effective  pressure 
for  each  test  by  adding  or  subtracting,  as  the  case  might  require, 
the  difference  between  the  actual  back- pressure  and  the  mean 
back-pressure  of  2.7  pounds  per  square  inch,  as  deduced  from 
all  the  tests. 

An  inspection  of  any  such  a  series  of  tests  having  a  wide  range 
of  expansions  will  show  that-  the  steam-consumption  decreases 
as  the  cut-off  is  shortened  till  a  minimum  is  reached,  usually  at 
£  to  £  stroke;  any  further  shortening  of  the  cut-off  will  be  accom- 
panied by  an  increased  steam-consumption,  which  may  become 
excessive  if  the  cut-off  is  made  very  short.  Some  insight  into 
the  reason  for  this  may  be  had  from  the  per  cent  of  water  in  the 
cylinder,  calculated  from  the  dimensions  of  the  cylinder  and  the 
pressures  in  the  cylinder  taken  from  the  indicator-diagram. 
The  method  of  the  calculation  will  be  given  in  detail  a  little  later 
in  connection  with  Hirn's  analysis.  It  will  be  sufficient  now  to 
notice  that  the  amount  of  water  in  the  cylinder  of  the  engine  of 
the  Michigan  at  release  increased  from  10.7  per  cent  for  a  cut-off 
at  i£  of  the  stroke  to  45.1  per  cent  for  a  cut-off  at  ^  of  the 
stroke.  Now  all  the  water  in  the  cylinder  at  release  is  vaporized 
during  the  exhaust,  the  heat  for  this  purpose  being  abstracted 
from  the  cylinder  walls,  and  the  heat  thus  abstracted  is  wasted, 
without  any  compensation.  The  walls  may  be  warmed  to  some 
extent  in  consequence  of  the  rise  of  pressure  and  temperature 
during  compression,  but  by  far  the  greater  part  of  the  heat 
abstracted  during  exhaust  must  be  supplied  by  the  incoming 
steam  at  admission.  There  is,  therefore,  a  large  condensation 
of  steam  during  admission  and  up  to  cut-off,  and  the  greater  part 


202  INFLUENCE    OF   THE    CYLINDER   WALLS 

of  the  steam  thus  condensed  remains  in  the  form  of  water  and 
does  little  if  anything  toward  producing  work.  This  may  be 
seen  by  inspection  of  the  table  of  results  of  DixwelPs  tests  on 
page  270.  With  saturated  steam  and  with  cut-off  at  0.217  °f  tne 
stroke,  52.2  per  cent  of  the  working  substance  in  the  cylinder 
was  water.  Of  this  19.8  per  cent  was  reevaporated  during  ex- 
pansion, and  32.4  per  cent  remained  at  release  to  be  reevaporated 
during  exhaust.  When  the  cut-off  was  lengthened  to  0.689  °f 
the  stroke,  there  was  27.9  per  cent  of  water  at  cut-off  and  23.9 
per  cent  at  release.  The  statement  in  percentages  gives  a 
correct  idea  of  the  preponderating  influence  of  the  cylinder  walls 
when  the  cut-off  is  unduly  shortened;  it  is,  however,  not  true 
that  there  is  more  condensation  with  a  short  than  with  a  long 
cut-off.  On  the  contrary,  there  is  more  water  condensed  in 
the  cylinder  when  the  cut-off  is  long,  only  the  condensation 
does  not  increase  as  fast  as  do  the  weight  of  steam  supplied  to 
the  cylinder  and  the  work  done,  and  consequently  the  conden- 
sation has  a  less  effect. 

Graphical    Representation.  —  The    divergence    of   the    actual 

expansion  line  from  the 
adiabatic  line  can  be 
shown  in  a  striking  manner 
by  plotting  the  former  on 
the  temperature-entropy 
diagram  as  shown  in 
Fig.  53  which  is  con- 
FlG" S2>  structed  from  the  indicator- 

diagram  in  Fig.  52,  shown  with  the  axes  of  zero  pressure  and 
zero  volume  drawn  in  the  usual  manner,  allowing  for  clearance 
and  for  the  pressure  of  the  atmosphere. 

In  order  to  undertake  this  construction  the  weight  of  steam 
per  stroke  W  as  determined  from  the  test  of  the  engine  during 
which  the  diagrams  were  taken,  must  be  determined,  and  the 
weight  of  steam  W0  caught  in  the  clearance  must  be  computed 
from  the  pressure  and  volume/,  the  beginning  of  compression. 
The  dry  steam  line  (Fig.  52)  is  drawn  by  the  following  process: 


GRAPHICAL   REPRESENTATION  203 

a  line  ae  is  drawn  at  a  convenient  pressure,  and  on  it  is  laid  off 
the  volume  of  W  +  W0  pounds  of  dry  steam  as  determined 
from  the  steam-table  to  the  proper  scale  of  the  drawing.  Thus 
if  se  is  the  specific  volume  of  the  steam  at  the  pressure  pe  the 
volume  of  steam  present  if  dry  and  saturated  would  be 

(W  +  W0)  s,. 

But  the  length  of  the  diagram  L,  in  inches  is  proportional  to 
the  piston  displacement  D  in  cubic  feet.  The  latter  is  obtained 
by  multiplying  the  area  of  the  piston  in  square  feet  by  its  stroke 
in  feet.  For  the  crank  end  the  net  area  of  the  piston  is  to  be  used, 
allowing  for  the  piston-rod.  Consequently  the  proper  abscissa, 

representing  the  volume  is  obtained  by  multiplying  by  —  ,  giving 

(W  +  Wn)  L 

D  ; 

and  of  this  all  except  s  is  a  constant  for  which  a  numerical  result 
can  be  found. 

The  diagram  shown  by  Fig.  52  was  taken  from  the  head  end 
of  the  high-pressure  cylinder  of  an  experimental  engine  in  the 
laboratory  of  the  Massachusetts  Institute  of  Technology.  The 
value  of  W  +  W0  was  found  to  be  0.075  °f  a  pound;  the  piston 
displacement  was  1.102  cubic  feet,  and  the  length  of  the  diagram 
was  3.69  inches;  consequently 

(W  +  W0)  L 

-^-°    -=0.251. 

The  line  ae  was  drawn  at  90  pounds  absolute  at  which  5  =  4.86 
cubic  feet  ;  the  length  of  the  line  ae  was  consequently 

0.251  X  4.86  =  1.22  inch. 

Neglecting  the  volume  of  the  water  present,  the  volume  of 
steam  actually  present  bore  the  same  ratio  to  the  volume  of  the 
steam  when  saturated,  that  ac  had  to  ae.  This  gave  in  the  figure 

at  c 


ac        0.04 

xe  =  —  =  —-22-  =  0.771 
ae       1.219 


\ 


204 


INFLUENCE   OF   THE   CYLINDER    WALLS 


To  plot  the  point  e  on  the  temperature- entropy  diagram, 
53,  we  may  find  the  temperature  at  90  pounds  absolute, 
namely,  320°  F.,  and  on  a  line  with  that  temperature  as  an  ordi- 
nate  we  may  interpolate  between  the  lines  for  constant  values 

of  x.      Other  points  can 
be  drawn  in  a  like  man- 
ner, and  the  curve  eg  can 
be  sketched  in;   showing 
that  the  steam  continues 
to  yield  heat  to  the  cylin- 
der walls  from  cut-off  till  c 
is  reached  on  Fig.  52,  and 
perhaps    a    trifle    longer. 
Beyond    c   the  steam  re- 
ceives heat  from  the  walls 
until  exhaust  opens. 
The  same  feature  is  exhibited  in  Fig.   52,   by  drawing  the 
adiabatic  line  xdn  from  the  point  of  cut-off.     The  point  d  can  be 
located  by  multiplying  the  length  ae,  which  represents  the  volume 
of  steam  in  the  cylinder  when  dry  by  the  value  of  x  after  adia- 
batic expansion  from  the  point  of  cut-off  n.     This  point  n  is 
readily  included  in  the  preceding  investigation,  so  that  xn  can  be 
determined.     Locating  n  on  the  temperature-entropy  diagram, 
Fig.  53,  we  may  draw  through  it  a  vertical  constant  entropy  line 
and  note  where  it  cuts  the  lines  corresponding  to  the  pressure 
lines  like  ae  in  Fig.  52,  and    interpolate  for  the  values    of  x. 
For  example,  the  entropy  at  n  in  Fig.  53  appears  to  be  1.36, 
and  at  320°  F.,  which  corresponds  to  90  pounds,  this  entropy 
line  gives  by  interpolation  0.78,  so  that  the  length  of  ad  is 

0.78  X  1.22  =  0.95. 

In  this  discussion  no  attempt  is  made  to  distinguish  the  moisture 
which  may  be  in  contact  with  the  wall  from  the  remainder  of 
steam  and  water  in  the  cylinder.  In  reality  that  moisture  has 
furnished  the  heat  which  the  cylinder  walls  acquire  during 
admission,  and  it  abstracts  heat  from  the  walls  during  the  expan- 


HIRN'S   ANALYSIS  205 

sion.  The  mixture,  moreover,  is  not  homogeneous,  because  the 
moisture  on  the  cylinder  walls  is  likely  to  be  colder  than  the 
steam,  though  naturally  it  cannot  be  warmer. 

Finally,  the  indicator-pencil  is  subject  to  a  friction  lag  that 
operates  to  produce  the  effect  shown  by  Figs.  52  and  53  and  is 
liable  to  exaggerate  them.  That  is  to  say,  the  pencil  draws  a 
horizontal  line  and  tends  to  remain  at  the  same  height  after  the 
steam-pressure  falls.  It  then  lets  go  and  falls  sharply  some 
little  time  after  the  valve  has  closed  at  cut-off.  Afterwards  it 
lags  behind  and  shows  a  higher  pressure  than  it  should. 

Hirn's  Analysis.  —  Though  the  methods  just  illustrated 
give  a  correct  idea  of  the  influence  of  the  walls  of  the  cylinder 
of  a  steam-engine,  our  first  clear  insight  into  the  action  of  the 
walls  is  due  to  Hirn,*  who  accompanied  his  exposition  by  quan- 
titative results  from  certain  engine  tests.  The  statement  of  his 
method  which  will  be  given  here  is  derived  from  a  memoir  by 
Dwelshauvers-Dery.f 

Let  Fig.  54  represent  the  cylinder  of  a  steam-engine  and  the 
diagram  of  the  actual  cycle.  For  sake  of  simplicity  the  diagram 
is  represented  without  lead  of  admission 
or  release,  but  the  equations  to  *be  deduced 
apply  to  engines  having  either  or  both. 
The  points  i,  2,  3,  and  o  are  the  points  of 
cut-off,  release,  compression,  and  admission. 
The  part  of  the  eye  le  from  o  to  i ,  that  is, 
from  admission  to  cut-off,  is  represented 


i 


by  a\  in  like  manner,  b,  c,  and  d  represent  FlG<  J4 

the  parts  of  the  cycle  during  expansion, 
exhaust,  and  compression.  The  numbers  will  be  used  as  sub- 
scripts to  designate  the  properties  of  the  working  fluid  under 
the  conditions  represented  by  the  points  indicated,  and  the 
letters  will  be  used  in  connection  with  the  operations  taking 
place  during  the  several  parts  of  the  cycle.  Thus  at  cut-off  the 

*  Bulletin  de  la  Soc.  Ind.  de  Mulhouse,  1873;  Theorie  Mechanique  de  la  Chaleur, 
vol.  ii,  1876. 

f  Revue  universelle  des  Mines,  vol.  viii,  p.  362,  1880. 


206  INFLUENCE    OF   THE   CYLINDER  WALLS 

pressure  is  pv  and  the  temperature,  heat  of  the  liquid,  heat  of 
vaporization,  quality,  etc.,  are  represented  by  tv  qv  rv  xv  etc. 
The  external  work  from  cut-off  to  release  is  Wt,  and  the  heat 
yielded  by  the  walls  of  the  cylinder  due  to  reevaporation  is  Qb. 

Suppose  that  M  pounds  of  steam  are  admitted  to  the  cylinder 
per  stroke,  having  in  the  supply-pipe  the  pressure  p  and  the 
condition  x;  that  is,  each  pound  is  x  part  steam  mingled  with 
i  —  x  of  water.  The  heat  brought  into  the  cylinder  per  stroke, 
reckoned  from  freezing-point,  is 

Q  =  M  (q  +  xr)    ......   (153) 

Should  the  steam  be  superheated  in  the  supply-pipe  to  the 
temperature  /„  then 

Q  =  M  [r  +  q  +  fcdfl  ......   (154) 

for  which  a  numerical  value  can  be  found  in  the  temperature- 
entropy  table. 

Let  the  heat-  equivalent  of  the  intrinsic  energy  of  the  entire 
weight  of  water  and  steam  in  the  cylinder  at  any  point  of  the 
cycle  be  represented  by  /;  thdh  at  admission,  cut-off,  release, 
and  compression  we  have 


>  =  (M  +M0)  (q,  +*,/>,);    ......   (156) 

2=  (M  +M9)(q9+x,p9);  .......   (157) 


in  which  p  is  the  heat-equivalent  of  the  internal  work  due  to 
vaporization  of  one  pound  of  steam,  and  M0  is  the  weight  of 
water  and  steam  caught  in  the  cylinder  at  compression,  calculated 
in  a  manner  to  be  described  hereafter. 

At  admission  the  heat-equivalent  of  the  fluid  in  the  cylinder 
is  70,  and  the  heat  supplied  by  the  entering  steam  up  to  the  point 
of  cut-off  is  Q.  Of  the  sum  of  these  quantities  a  part,  AWa,  is 
used  in  doing  external  work,  and  a  part  remains  as  intrinsic 
energy  at  cut-off.  The  remainder  must  have  been  absorbed  by 


HIRN'S   ANALYSIS  207 

the  walls  of  the  cylinder,  and  will  be  represented  by  Qa.     Hence 

Q.  =  Q  +/.-/,-  AW.. 

From  cut-off  to  release  the  external  work  Wb  is  done,  and  at 
release  the  heat-equivalent  of  the  intrinsic  energy  is  72.  Usually 
the  walls  of  the  cylinder,  during  expansion,  supply  heat  to  the 
steam  and  water  in  the  cylinder.  To  be  more  explicit,  some 
of  the  water  condensed  on  the  cylinder  walls  during  admission 
and  up  to  cut-off  is  evaporated  during  expansion.  This  action 
is  so  energetic  that  /2  is  commonly  larger  than  Ir  Since  heat 
absorbed  by  the  walls  is  given  a  positive  sign,  the  contrary  sign 
should  be  given  to  heat  yielded  by  them;  it  is,  however,  con- 
venient to  give  a  positive  sign  to  all  the  interchanges  of  heat  in 
the  equations,  and  then  in  numerical  problems  a  negative  sign 
will  indicate  that  heat  is  yielded  during  the  operation  under 
consideration.  For  expansion,  then, 

Qt  =  It-  /,  -AW,. 

During  the  exhaust  the  external  work  Wc  is  done  by  the  engine 
on  the  steam,  the  water  resulting  from  the  condensation  of  the 
steam  in  the  condenser  carries  away  the  heat  M</4,  the  cooling 
water  carries  away  the  heat  G  (qt  —  #),  and  there  remains  at 
compression  the  heat-  equivalent  of  intrinsic  energy  72.  So  that 


Q.  -  7,  -  7.  -  Mqt  -G(qk-  q<)  +  AWC, 

in  which  </4  is  the  heat  of  the  liquid  of  the  condensed  steam,  and 
G  is  the  weight  of  cooling  water  per  stroke  which  has  on  entering 
the  heat  of  the  liquid  qt,  and  on  leaving  the  heat  of  the  liquid  qk. 

During  compression  the  external  work  Wd  is  done  by  the 
engine  on  the  fluid  in  the  cylinder,  and  at  the  end  of  compression, 
i.e.,  at  admission,  the  heat-equivalent  of  the  intrinsic  energy  is  70. 
Hence 

Q,  -/,-/.+  AWt. 

It  should  be  noted  (Fig.  54)  that  the  work  Wa  is  represented 


208 


INFLUENCE    OF   THE    CYLINDER   WALLS 


by  the  area  which  is  bounded  by  the  steam  line,  the  ordinates 
through  o  and  i  and  by  the  base  line.  And  in  like  manner  the 
works  Wb,  WC)  and  Wd  are  represented  by  areas  which  extend 
to  the  base  line.  In  working  up  the  analysis  from  a  test  the 
line  of  absolute  zero  of  pressure  may  be 
drawn  under  the  atmospheric  line  as  in 
Fig.  55,  or  proper  allowance  may  be 
made  after  the  calculation  has  been  made 
with  reference  to  the  atmospheric  line. 
For  convenience  these  four  equa- 
tions  will  be  assembled  as  follows: 


Atmospheric  line 


Qa  =  Q  +I0-I1-AWa     ......  (159) 

Qb  =  I,-  I2-  AW>     ........  (160) 

QC  =  I2-I3-  Mq,  -G(qk-  %)  +  AWC  .  (161) 

Qd  =  /3  -/0  +AWd     ........  (162) 

A  consideration  of  these  equations  shows  that  all  the  quanti- 
ties of  the  right-hand  members  can  be  obtained  directly  from 
the  proper  observations  of  an  engine  test  except  the  several 
values  of  /,  the  heat-  equivalents  of  the  intrinsic  energies  in  the 
cylinder.  These  quantities  are  represented  by  equations  (155) 
to  (158),  in  which  there  are  five  unknown  quantities,  namely, 

*o>   xv  xv  xv  and  Mo- 

Let  the  volume  of  the  clearance-space  between  the  valve  and 

the  piston  when  it  is  at  the  end  of  its  stroke  be  F0;  and  let  the 
volumes  developed  by  the  piston  up  to  cut-off  and  release  be 
Vl  and  F2;  finally,  let  F3  represent  the  corresponding  volume 
at  compression.  The  specific  volume  of  one  pound  of  mixed 
water  and  steam  is 

•U   =   XU    +  <ry 

and  the  volume  of  M  pounds  is 

V  =  Mv  =  M  (xu  +  <7). 


HIRN'S    ANALYSIS 


209 


At  the  points  of  admission,  cut-off,  release,  and  compression, 

F0  =  M0  (*A  +  o-) (163) 

F0  +  V,  =  (M  +  Jf  0)  (a^  +  «r) (164) 

F0  +  F2  =  (M  +  M0)  (*A  -f  o-) (165) 

F0  +  F3  =  M0  (*,«,  +  o-) (166) 

There  is  sufficient  evidence  that  the  steam  in  the  cylinder 
at  compression  is  nearly  if  not  quite  dry,  and  as  there  is  com- 
paratively little  steam  present  at  that  time,  there  cannot  be 
much  error  in  assuming 

#3=1. 

This  assumption  gives,  by  equation  (166), 

in  which  73  is  the  density  or  weight  of  one  cubic  foot  of  dry 
steam  at  compression. 

Applying  this  result  to  equations  (263)  to  (265)  gives 

*»=  ir!r— r  •• (j68) 


(169) 


(M  +  M0)  u, 


(M  +  M,)  u,       „, 

We  are  now  in  condition  to  find  the  values  of  /0,  Iv  72,  and 
73,  and  consequently  can  calculate  all  the  interchanges  of  heat 
by  equations  (159)  to  (162). 

Should  the  value  of  x  in  any  case  appear  to  be  greater  than 
unity  it  indicates  that  the  steam  is  superheated;  this  may  happen 
for  XQ,  and  then  as  the  weight  of  steam  M 0  is  relatively  small, 
and  as  the  superheating  is  usually  slight,  it  will  be  sufficient  to 
make  x0  equal  to  unity.  It  is  unlikely  to  be  the  case  for  xl  or  xv 
even  though  the  steam  is  strongly  superheated  in  the  steam- pipe; 


210  INFLUENCE   OF   THE    CYLINDER    WALLS 

should  the  computation  give  a  value  slightly  larger  than  unity 
the  steam  may  be  assumed  to  be  dry  without  appreciable  error, 
and  the  work  may  proceed  as  indicated.  If  in  the  use  of  very 
strongly  superheated  steam  a  computed  value  of  x2  is  appre- 
ciably larger  than  unity,  we  may  replace  the  equation  (166)  by 

V.  +  V2  =  (M  +  M9)  vv 

where  v2  is  the  specific  volume  of  superheated  steam;  conse- 
quently 

„  =Y*-+-L. 

M  +M0 

By  aid  of  the  temperature-entropy  table  we  may  find  (by  inter- 
polation if  necessary)  the  corresponding  temperature  /2  and  the 
value  of  the  heat-contents  or  total  heat.  The  heat-equivalent 
of  the  intrinsic  energy  is  then  equal  to  this  quantity  minus  Ap2v2. 

In  the  diagram,  Fig.  54,  the  external  work  during  exhaust  is 
all  work  done  by  the  piston  on  the  fluid,  since  the  release  is 
assumed  to  be  at  the  end  of  the  stroke.  If  the  release  occurs 
before  the  end  of  the  stroke,  some  of  the  work,  namely,  from 
release  to  the  end  of  the  stroke,  will  be  done  by  the  steam  on  the 
piston,  and  the  remainder,  from  the  end  of  the  stroke  back  to 
compression,  will  be  done  by  the  piston  on  the  fluid.  In  such 
case  Wc  will  be  the  difference  between  the  second  and  the  first 
quantities.  If  an  engine  has  lead  of  admission,  a  similar  method 
may  be  employed;  but  at  that  part  of  the  diagram  the  curves  of 
compression  and  admission  can  be  distinguished  with  difficulty, 
if  at  all,  and  little  error  can  arise  from  neglecting  the  lead. 

The  several  pressures  at  admission,  cut-off,  release,  and 
compression  are  determined  by  the  aid  of  the  indicator-diagram, 
and  the  pressures  in  the  steam-pipe  and  exhaust-pipe  or  con- 
denser are  determined  by  gauges.  The  weight  M  of  steam 
supplied  to  the  cylinder  per  stroke  is  best  determined  by  con- 
densing the  exhaust-steam  in  a  surface-condenser  and  collecting 
and  weighing  it  in  a  tank.  If  the  engine  is  non-condensing,  or 
if  it  has  a  jet-condenser,  or  if  for  any  reason  this  method  cannot 


HIRN'S    ANALYSIS  211 

be  used,  then  the  feed-  water  delivered  to  the  boiler  may  be  deter- 
mined instead.  The  cooling  or  condensing  water,  either  on 
the  way  to  the  condenser  or  when  flowing  from  it,  may  be  weighed, 
or  for  engines  of  large  size  may  be  measured  by  a  metre  or  gauged 
by  causing  it  to  flow  over  a  weir  or  through  an  orifice.  The 
several  temperatures  /4,  /,-,  and  tk  must  be  taken  by  proper  ther- 
mometers. When  a  jet-condenser  is  used,  and  the  condensing 
water  mingles  with  the  steam,  /4  is  identical  with  tk.  The  quality 
x  of  the  steam  in  the  supply-pipe  must  be  determined  by  a  steam- 
calorimeter.  A  boiler  with  sufficient  steam-space  will  usually 
deliver  nearly  dry  steam;  that  is,  x  will  be  nearly  unity.  If 
the  steam  is  superheated,  its  temperature  tt  may  be  taken  by  a 
thermometer. 

Let  the  heat  lost  by  radiation,  conduction,  etc.,  be  Qe\  this 
is  commonly  called  the  radiation.  Let  the  heat  supplied  by 
the  jacket  be  Qj.  Of  the  heat  supplied  to  the  cylinder  per  stroke, 
a  portion  is  changed  into  work,  a  part  is  carried  away  by  the 
condensed  steam  and  the  cooling  or  condensing  water,  and 
the  remainder  is  lost  by  radiation;  therefore 

Qe=Q  +  Qj-Mqi-G(qk-qi)-A(Wa+Wb-Wc-Wd)   .   (171) 

The  heat  Qj  supplied  by  a  steam-jacket  may  be  calculated 
by  the  equation 

Qj  =  m  (*V  +  f  -  g")    .     .     .     .       (172) 


in  which  m  is  the  weight  of  water  collected  per  stroke  from  the 
jacket;  xfy  r',  and  <f  are  the  quality,  the  heat  of  vaporization, 
and  the  heat  of  the  liquid  of  the  steam  supplied;  and  (fr  is  the 
heat  of  the  liquid  when  the  water  is  withdrawn.  When  the 
jacket  is  supplied  from  the  main  steam-pipe,  x9  is  the  same  as 
the  quality  in  that  pipe.  When  supplied  direct  from  the  boiler, 
x*  may  be  assumed  to  be  unity.  If  the  jacket  is  supplied 
through  a  reducing-valve,  the  pressure  and  quality  may  be 
determined  either  before  or  after  passing  the  valve,  since  throt- 
tling does  not  change  the  amount  of  heat  in  the  steam.  Should 


212  INFLUENCE   OF   THE    CYLINDER   WALLS 

the  steam  applied  to  the  jacket  be  superheated  from  any  cause, 
we  may  use  the  equation 


Qj  _  m  {r>  +  cf  +  Cp  (t,'  -  f)  -g"}.    .    .     (173) 

in  which  r1  and  cf  are  the  heat  of  vaporization  and  heat  of 
the  liquid  of  saturated  steam  at  the  temperature  ^,  and  txf  is 
the  temperature  of  the  superheated  steam. 

Equation  (171)  furnishes  a  method  of  calculating  the  heat 
lost  by  radiation  and  conduction;  but  since  Qe  is  obtained  by 
subtraction  and  is  small  compared  with  the  quantities  on  the 
right-hand  side  of  the  equation,  the  error  of  this  determination 
may  be  large  compared  with  Qe  itself.  The  usual  way  of  deter- 
mining Qe  for  an  engine  with  a  jacket  is  to  collect  the  water 
condensed  in  the  jacket  for  a  known  time,  an  hour  for  example, 
when  the  engine  is  at  rest,  and  then  the  radiation  of  heat  per 
hour  may  be  calculated.  If  it  be  assumed  that  the  rate  of  radia- 
tion at  rest  is  the  same  as  when  the  engine  is  running,  the  radia- 
tion for  any  test  may  be  inferred  from  the  time  of  the  test  and  the 
determined  rate.  But  the  engine  always  loses  heat  more  rapidly 
when  running  than  when  at  rest,  so  that  this  method  of 
determining  radiation  always  gives  a  result  which  is  too 
small. 

If  a  steam-engine  has  no  jacket  it  is  difficult  or  impossible 
to  determine  the  rate  of  radiation.  The  only  available  way 
appears  to  infer  the  rate  from  that  of  some  similar  engine  with 
a  jacket.  Probably  the  best  way  is  to  get  an  average  value  of 
Qe  from  the  application  of  equation  (171)  to  a  series  of  care- 
fully made  tests. 

It  is  well  to  apply  equation  (171)  to  any  test  before  beginning 
the  calculation  for  Hirn's  analysis,  as  any  serious  error  is  likely  to 
be  revealed,  and  so  time  may  be  saved. 

When  the  radiation  Qe  is  known  from  a  direct  determination 
of  the  rate  of  radiation,  we  may  apply  Hirn's  analysis  to  a  test 
on  an  engine  even  though  the  quantities  depending  on  the  con- 
denser have  not  been  obtained.  For  from  equation  (171) 


HIRN'S   ANALYSIS  213 

-Mqt  -  G  (ft,  -  ft)  =  Q,  -  Q -Qi  +  A (Wa  +  Wt-  W<-  Wd), 

and  consequently 

Q,  =  /,  -  /,  -  Q  -  Qi  +  Qe  +  A  (Wa  +  Wb  -  Wd)  .  .  (174) 

Thus  it  is  possible  to  apply  the  analysis  to  a  non-con- 
densing engine  or  to  the  high-pressure  cylinder  of  a  compound 
engine. 

It  is  apparent  that  the  heat  Qc,  thrown  out  from  the  walls 
of  the  cylinder  during  exhaust,  passes  without  compensation 
to  the  condenser,  and  is  a  direct  loss.  Frequently  it  is  the 
largest  source  of  loss,  and  for  this  reason  Him  proposed  to  make 
it  a  test  of  the  performance  and  perfection  of  the  engine;  but 
such  a  use  of  this  quantity  is  not  justifiable,  and  is  likely  to 
lead  to  confusion. 

The  heat  Qb  that  is  restored  during  expansion  is  supplied  at 
a  varying  and  lower  temperature  than  that  of  the  source  of  heat, 
namely,  the  boiler,  and,  though  not  absolutely  wasted,  is  used 
at  a  disadvantage.  It  has  been  suggested  that  an  early  com- 
pression, as  found  in  engines  with  high  rotative  speed,  warms 
up  the  cylinder  and  so  checks  initial  condensation,  thereby 
reducing  Qa  and  finally  Qc  also.  Such  a  storing  of  heat  during 
compression  and  restoring  during  expansion  is  considered  to 
act  like  the  regenerator  of  a  hot-air  engine,  and  to  make  the 
efficiency  of  the  actual  cycle  approach  the  efficiency  of  the  ideal 
cycle  more  nearly  than  would  be  the  case  without  compression. 
It  does  not,  however,  appear  that  engines  of  that  type  have 
exceeded,  if  they  have  equalled,  the  performance  of  slow-speed 
engines  with  small  clearance  and  little  compression. 

Application.  —  In  order  to  show  the  details  of  the  method  of 
applying  Hirn's  analysis  the  complete  calculation  for  a  test 
made  on  a  small  Corliss  engine  in  the  laboratory  of  the  Massa- 
chusetts Institute  of  Technology  will  be  given.  Its  usefulness  is 
mainly  as  a  guide  to  any  one  who  may  wish  to  appry  the  method 
for  the  first  time. 


214 


INFLUENCE   OF   THE   CYLINDER   WALLS 


Diameter  of  the  cylinder 8  inches. 

Stroke  of  the  piston 2  feet. 

Piston  displacement:  crank  end 0.6791  cu.  ft. 

head  end 0.7016  "     ' 

Clearance,  per  cent  of  piston  displacement : 

crank  end 3.75 

head  end 5.42 

Boiler-pressure  by  gauge 77.4  pounds. 

Barometer 14.8       " 

Condition  of  steam,  two  per  cent  of  moisture. 
Events  of  the  stroke: 

Cut-off:  crank  end 0.306  of  stroke. 

head  end 0.320         " 

Release  at  end  of  stroke. 

Compression:  crank  end    .    .    .    . 0.013  of  stroke. 

head  end 0.0391        " 

Duration  of  the  test,  one  hour. 

Total  number  of  revolutions 3692 

Weight  of  steam  used 548  pounds. 

Weight  of  condensing  water  used 14,568  " 

Temperatures : 

Condensed  steam /4  =  141°.!  F. 

«        Condensing  water:  cold /i  =    52°. 9  F. 

warm tk  =    88°.3  F. 

*  ABSOLUTE     PRESSURES,     FROM     INDICATOR-DIAGRAMS,     AND 
CORRESPONDING   PROPERTIES   OF  SATURATED   STEAM. 


CRANK  END. 


HEAD  END. 


Cut-off  .  .  . 
Release  .  .  . 
Compression . 
Admission 


83.6 
29.2 
14.8 
21.8 


284.6 
217.8 
181.1 
201.5 


813.0 
864.8 
893.2 
877.4 


5.190 
13.924 
26.464 
18.344 


83.3 
3i-9 
14.8 
29.8 


284.4 
222.9 
181.1 
219.0 


813.2 
860.8 
893.2 
863.9 


5.207 

12.804 
26.464 

13.664 


*  These  values  are  taken  from  the  first  edition  of  the  Tables  of  Properties  of 
Saturated  Steam. 


APPLICATION 


215 


MEAN    PRESSURES,    AND    HEAT-EQUIVALENTS    OF    EXTERNAL 

WORKS. 


CRANK  END. 

HEAD  END. 

Mean  Pressures. 

Equivalents  of 
Work. 

Mean  Pressures. 

Equivalents  of 
Work. 

Admission     .... 
Expansion     .... 
Exhaust     
Compression     .    .    . 

87.7 

44-5 
14.8 

18.3 

3.369 
3-877 
1.836 
0.0290 

89.3 
47-i 
14.8 

21.8 

3-7II 
4-159 
l.847 
0.1104 

VOLUMES,   CUBIC   FEET. 


CRANK  END. 

HEAD  END. 

At  cut-off,       ^o+^i   

O.  2333 

O   2626 

At  release,       V0  +  Vt  

o.  7046 

o.  7306 

At  compression,  VQ-\-  V3    

O.O343 

O  06^  ^ 

At  admission,      V0    

0.02550 

0.03806 

At  the  boiler-pressure,  92.1  pounds  absolute,  we  have 

r  =  888.4,  <7  =  291.7. 

The  steam  used  per  stroke  is 


M 


548 


2    X  3692 


=  0.0742  pound. 


The  steam  caught  in  the  clearance  space  at  compression,  on 
the  assumption  that  the  steam  is  then  dry  and  saturated,  is 
obtained  by  multiplying  the  mean  volume  at  that  point  by  the 
weight  of  one  cubic  foot  of  steam  at  the  pressure  at  compression, 
which  is  0.03781  of  a  pound. 


,      1/f  0.0343    +  0.0655  o  f 

.  •  M 0  =  M "  X  0.03781  =  0.0019  °f  a  pound; 

M  +  M0  =  0.0742  +  0.0019  =  0.0761  pound. 
The  condensing  water  used  per  stroke  is 
~  14568 


2    X  3692 


=  1-973- 


2i6  INFLUENCE   OF   THE   CYLINDER    WALLS 

Q  =  M  (xr  +  q)  =  0.0742(0.98  X  888.3  +  291-8)  =  86.243; 

V 


(0.02550     +   0.038O6) 


°      0.0019  X  Ml8-344  +13-664)       62.4X^(18.344+13-664) 
=  1-043. 

This  indicates  that  the  steam  is  superheated  at  admission. 
Such  may  be  the  case,  or  the  appearance  may  be  due  to  an 
error  in  the  assumption  of  dry  steam  at  compression,  or  to  errors 
of  observation.  It  is  convenient  to  assume  x^=  i. 


oc.  — 


~  (M  +  M0)  «,      *,  ' 

(0.2333     +  0.2626) 


0.0761  X  i  (5.190  +  5.207)      62.4  X  £(5.190  +  5-2°7) 
=  0.6236. 

V,  +  V,  o_. 

~~  (M  +  M9)  u,f    u2   ' 

j  (0.7046  +  0.7396)  i 


2      0.0761  Xi(i3-924  +12.804)       62.4  Xi(I3-924  +12.804) 
=  0.7088. 

^o  =  ^o(?o  +*</>(>); 

^o  =  i  X  0.0019  [201.5  +  2I9-°  +  I-°°  (877-4  +  863.9)] 

=  2.054. 
Jt-  (M  +M0)(?1  +^J; 

Jj    =    J    X  0.0761    [284.6    +   284.4    +  0.6236    (8I3.0+8I3.2)] 
=    60.238. 

J2=  (M+M9)(q9+xjJ; 

I2  =  \  x  0.0761  [217.8+222.0  +  0.7088  (864.8  +  861.8)] 
=  63.311. 


0.0019  (181.1  +  893.2)  =  2.041. 


APPLICATION  217 

Q«  =  Q  +I0-I1-AWa', 

/.  Qa  =  86.243  +  2.054  -  60.238  -  i  (3.369+3.711)  =  24.51^ 
Qb  =  7t  -  72  -  AWb; 

.-.  Q,  =  60.238  -  63.311  --  i  (3.877  +  4-159)  =  - 

<2C  =  72  -  J3  -  M?4  -G(qk-  q<)  +  AJFe; 

•"•  Qc  =  63.311  -  2.041  -  0.0742  x  109.3 

-  1.973  (56.35  -  21.01)  +  i  (1.836  +  1.847) 

- 14.721. 

Q*  =  /i  -  A  +  ^TFk; 

.*.  Qrf  =  2.041  —  2.054  +  J  (0.0299  +  0-1104)  =  0.157. 
Qe  =  Qa+Q*+Qc+Q*  =  2.764. 

Also,  equation  (171)  for  this  case  gives 
Qe  =  Q  -  Mq,  -  G  (qk  -  q<)  -  AW 

=  86.243  — 8.110—69.723  — (3.540+4.018  — 1.841  —0.070) 
=  86.243-8.110-69.723-5.647  =  2.764. 

It  is  to  be  remembered  that  the  heat  lost  by  radiation  and 
conduction  per  stroke,  when  estimated  in  this  manner,  is  affected 
by  the  accumulated  errors  of  observation  and  computation, 
which  may  be  a  large  part  of  the  total  value  of  Qe. 

Dropping  superfluous  significant  figures,  we  have  in  B.T.U. 

Q   =  86.2,  Qa  =  24.5,  Qb  =  -  7.1, 

Qe  =  -  14.7,  Qd  -  -06,  Qe  =  2.8. 

Noting  that  5.647  are  the  B.T.U.  changed  into  work  per  stroke 
and  3692  the  total  revolutions  the  horse-power  of  the  engine  is 

778  X  5-647  X  3692  X  2  =  l6    -  H  p  . 
60  X  33000 

and  the  steam  per  horse-power  per  hour  is 

rij  =  33'5  pounds' 

For  data  and  results  of  this  test  and  others  see  Table  IV. 


21 8 


INFLUENCE    OF   THE    CYLINDER   WALLS 


TABLE  IV. 

APPLICATION  OF  HIRN'S  ANALYSIS  TO  A  SMALL  CORLISS  ENGINE  AT  THE  MASSACHUSETTS 
INSTITUTE  OF  TECHNOLOGY. 

DIAMETER,  8  INCHES;  STROKE,  24  INCHES. 

"O 

I 

S 

3 

Admission. 
Po 

W 
B 

00  t^  O>00  00 

d  >o  TJ-  -4  dv 

•spunod 
'jnoq  jad  jaMod 
-asaoq  jad  ui^a^g 

COO   O  co  «0 

•<foo°  dv  >o  co 

^"  CO  CO  CO  CO 

1 

"S   . 

•»"<»! 

COOO    M    CO  >0 
VO  O    *^  M    CO 

•O  oo'  00   M  so 

W 
U 

oo  i^  o-oooo 

•JOJJ3        % 

PUB  uoDBipByOi 

?:fs? 

Compression. 
Ps 

w 
B 

00  *^  0,00  00 

•uoissajdmoD 
Suunp  sjpJM     o 
/tq  paqjosqy 

d  o  o'  o'  o" 

W 

oo  »^  0.0000 

•jsn'eqxa 
Suunp  sjpM     Q) 
'Aq  pappt^ 

COOO  t^-  co  M 

so   0^0  J 

L 

w" 

ffi 

00  t^tr>CQ   0, 

so  d\  d  co  M 

"uoisuBdxa 
Suurip  sjpM     Q, 
'  ^q  P3PP!A 

*^  O   >0  TJ-  o> 
NSO   MSO   0 

w 

cj 

co  r^vo  oo  N 

•UOISStUlpB 

Suunp  si  [EM      « 
Aq  paqjosqv0* 

M  O  CO     O\    W 
O\  N    IN    CO  >0 

1* 

u 

w 

B 

•UTB3}S  JSIOUI 

jo  spunod     O1 

0   H   0   0   •* 

so   N  1^  O   co 
t^oo  t^oo  oo 

w 
u 

M    t>.  C*    M  SO 

Heat-equivalents  of  work. 
B.T.U. 

Aig 

31* 

a 

W 
B 

00   •*  O-vO   O 

o'  d  d  d  d 

1^00   t^  t^OO 

W 

U 

M  10  e«  o-  O\ 

d  o  d  o  d 

•spunod  'a3nE9 
Aq  aanss3ad-j3[iog      ^ 

t^O  >0  0.  -<t 

CO   cooo'  M'  r^. 
so   t^sO   t^  !•-• 

li 

w 
B 

1^00  00  00  00 

•qoui  aaunbs  aqj  uo 
spunod  'j3}3iuo.reg 

00  r-  O.OO  00 

w 

u 

1^  W   t  O  so 

H    M    10  CO  CO 
00  00  00  00  00 

rf 

2% 

ii 

6  $ 
HO 

s?;4^D  -- 

CO 
CO  O   O     -co 

^•sO    t^  COOO 

Expansion  . 
AWb 

w 

^f  CO  Tf  Os  O\ 
00  00  SO    M    «0 

-Suisuapuo^)        "^ 

W  OO   W  so   O- 

w 
u 

w  00    O    M    t^ 
M    N    M    1000 

-o 

w 
d 

O»SO    CO  !>•   H 

r~.oo  co  M  M 

0    M    M     M     CO 

•UIB3JS 

pasuapuo^        ""* 

SO  10  O  00   M 
00  0  i  od   «  M 

M     CO   M     CO   •^~ 

w 
o 

t^  >0  H  00    O\ 

•UIE31S  UI            H 
Suiiuud  JO  JU33  J3(J 

, 

Com- 
pression. 

w 
B 

t--.sO   •*  0   Ov 

•  ;;iunod  'aajBAV-3ut 
-.;uopuoo  jo  jqSia^Y 

CO  t^  Tf  H  00 

co  O   T)-OO   T)- 

Events  of  the  stroke  — 
per  cent  of  stroke  from  beginni 

sj 

Release. 

M 
M 

§§§§§ 

•spunod  'pasn 
uiE3}S  jo  }qSw.M. 

CO  t»  O   >000 
•<t  <M    t-  Ov  "t 
M    CO  M    W    10 

o 

88888 

•suopnioAaa 
jo  aaquinu  l*loj. 

O.  O.  O.  0    M 
co  O   co  *^-  O\ 

CO  so  00  so  sc 

H    CO  M    C1    CO 

Cut-off. 

B 

0    M    0   «OO 

Ov  W    !O  O»   fS 
H     M    M    CO 

•ssjnuuu  'uopnanQ 

S5SM 

w 
u 

0   W   0  «OSQ 
O   P<   *o  Ov  O 

•aaquw^                |     _te*co-*io 

•a.Hiimi\                             r4C4CO*<lO 

SUPERHEATED    STEAM  219 

Effect  of  Varying  Cut-off.  —  An  inspection  of  the  interchanges 
of  heat  shows  that  the  values  of  Qa,  the  heat  absorbed  by  the 
walls  during  admission,  increase  regularly  as  the  cut-off  is 
lengthened,  and  that  the  heat  returned  during  expansion  decreases 
at  the  same  time,  so  that  there  is  a  considerable  increase  in  the 
value  of  the  heat  Qc  which  is  rejected  during  exhaust.  Never- 
theless there  is  a  large  gain  in  economy  from  restricting  the 
cut-off  so  that  it  shall  not  come  earlier  than  one- third  stroke. 
Unfortunately  tests  on  this  engine  with  longer  cut-off  than  one- 
third  stroke  have  not  been  made,  and  consequently  the  poorer 
economy  for  long  cut-off  cannot  be  shown  for  this  engine  as  for 
the  engine  of  the  Michigan. 

Hallauer's  Tests.  —  In  Table  V  are  given  the  results  of  a 
number  of  tests  made  by  Hallauer  on  two  engines,  one  built  by 
Hirn  having  four  flat  gridiron  valves,  and  the  other  a  Corliss 
engine  having  a  steam-jacket.  Two  tests  were  made  on  the 
former  with  saturated  steam  and  six  with  superheated  steam. 
Three  tests  were  made  on  the  latter  with  saturated  steam  and 
with  steam  supplied  to  the  jackets.  These  tests  have  a  historic 
interest,  for  though  not  the  first  to  which  Hirn's  analysis  was 
applied,  they  are  the  most  widely  known,  and  brought  about  the 
acceptance  of  his  method.  They  have  also  a  great  intrinsic 
value,  as  they  exhibit  the  action  of  two  different  methods  of 
ameliorating  the  effect  of  the  action  of  the  cylinder  walls,  namely, 
by  the  use  of  superheated  steam  and  of  the  steam-jacket.  In  all 
these  tests  there  was  little  compression,  and  Qd,  the  interchange 
of  heat  during  compression,  is  ignored. 

Superheated  Steam.  —  Steam  from  a  boiler  is  usually  slightly 
moist,  x,  the  quality,  being  commonly  0.98  or  0.99.  Some  boilers, 
such  as  vertical  boilers  with  tubes  through  the  steam  space,  give 
steam  which  is  somewhat  superheated,  that  is,  the  steam  has  a 
temperature  higher  than  that  of  saturated  steam  at  the  boiler- 
pressure.  Strongly  superheated  steam  is  commonly  obtained  by 
passing  moist  steam  from  a  boiler  through  a  coil  of  pipe,  or  a 
system  of  piping,  which  is  exposed  to  hot  gases  beyond  the 
boiler. 


22O 


INFLUENCE    OF   THE   CYLINDER   WALLS 


H 


2    1 


£3     ^ 


•«loajs  »d               « 
papafaa  -n'i'a      o 

t>.  ON 

•<*•  •* 

10  O   O     HI     t^  t-» 

t-«  t^vO  00  00     1 

Tf  rj-  Th 

•*    Tt-    Tj- 

1            a 

• 

M    ON  M 
tO  Tt-    TJ- 

°« 

II     s 

«3  u 

10  O 

vO      •    ts    ro^O      • 

\O    fO  M 

H     M 

1H        •     M     M     H        • 

M     M     M 

si 

il        6 

^'S 

0      Tt 

M 
10  t^OO    to  C4       • 

fOOO     O 

M     W) 

M      M 

N     ON  t^-  O    Tt    I 
M                     H     M     1 
-J— 

CS    ONOO 

M 

"S5 

II              o 

O    «*5 
10  t^ 

Tt         •       O          •          •           • 

m  O   rf 

00     •   «     •     •     • 

r^  to  O 

8 

«                6 

fO  ON 

Tt        •      O          •         •         ' 

Tt     M      -t 

OO    fO 
w  w 

(N         •      M 
^        .     M        •        •        • 

VO      M     IO 

CS     CM     M 

•ajmnui  jad 

•j  *H  «d  -n-i/a 

«*5  O 

VO  ON 

NO    to  O    w    O 

ON  ON  <N    Tj-00       • 
N    0*    PO  CO  PD     • 

•spunod  'anoq  »d 
•d  *H  aad  u»«ajs 

ON  to 

O    t^»  M    CS    W    ON 

00    t^-00 

ON  N 

\O   to  t—  00    O   t^ 

t^  t^  t^. 

•aaMod-asaoji 

•*vO 

vd  4 

O    ro 

O    O    rj-  toO    CO 

M    TJ-   W    •*  ON  *>• 
M     fT)  Tj-    (Nl   OO     t^ 

VO     M     ON 

CO  ON  10 
O     CS    to 

•tpui  3.n3nbs  aad 
spunod  '3»n[osqK 
'ajnssaud-jpEg 

0    <N 

r^.  t^-  w  t~»  to    • 

M      TtVO 

f*5  to 

w   cs  to  ts   w 

N     N    M 

•ipui  ajEnbs  jad 
spunod  'ainjosqe 
'aanssajd-aajtOH 

t"~  O 

M    O  \O    ^vo    N 

RS 

M     M     QNOO     M     (S 

t^  t^\O  vO    t^.sO 

•snoisuEdx-hf 

M    ON 

vO*   ro 

H    1^  ON  <N)     CS    to 
vO    T}-  f*5  W    N    ro 

W  00  O 

M 

•ojnniui 
jad  «uoi)n[OA9^ 

•*vO 

O    O    w    ro  M    O 

Tt  M    re 

0    O 

re  fO 

O    0    0    0    0    0 

0     M     ON 
to  10  Tt 

••«q«j 

'iuc3}s  paieaqjadns 
'aan^cjadtaax 

r^  ONOO    f^OO  00 
OO     *H    rj-   r<J  M     n 
CO  Tj-  Tj-  rf   rj-  rt 

•aoptpaoo 

pajB9qjadn§ 

pavwpuf 

«  04 

* 

*SS 

.N 


2  .2 


H    jg 

o 

ti 

Cj 

D- 


SUPERHEATED    STEAM  221 

Superheated  steam  may  yield  a  considerable  amount  of  heat 
before  it  begins  to  condense;  consequently  where  superheated 
steam  is  used  in  an  engine  a  portion  of  the  heat  absorbed  by  the 
walls  during  admission  is  supplied  by  the  superheat  of  the  steam 
and  less  condensation  of  steam  occurs.  This  is  very  evident  in 
DixwelPs  tests  given  by  Table  XXV,  on  page  271,  where  the 
water  in  the  cylinder  at  cut-off  is  reduced  from  52.2  per  cent  to 
27.4  per  cent,  when  the  cut-off  is  two-tenths  of  the  stroke,  by 
the  use  of  superheated  steam;  with  longer  cut-off  the  effect  is 
even  greater.  This  reduction  of  condensation  is  accompanied 
by  a  very  marked  gain  in  economy. 

The  way  in  which  superheated  steam  diminishes  the  action 
of  the  cylinder  walls  and  improves  the  economy  of  the  engine  is 
made  clear  by  Hallauer's  tests  in  Table  V.  A  comparison  of 
tests  i  and  3,  having  six  expansions,  shows  that  the  heat  Qa 
absorbed  during  admission  is  reduced  from  28.3  to  22.4  per  cent 
of  the  total  heat  supplied,  and  that  the  exhaust  waste  is  corre- 
spondingly reduced  from  21.6  to  12.5  per  cent.  A  similar 
comparison  of  tests  2  and  5,  having  nearly  four  expansions, 
shows  even  more  reduction  of  the  action  of  the  cylinder  walls. 
The  effect  on  the  restoration  of  heat  Qb  during  expansion  appears 
to  be  contradictory:  in  one  case  there  is  more  and  in  the  other 
case  less.  It  does  not  appear  profitable  to  speculate  on  the 
meaning  of  this  discrepancy,  as  it  may  be  in  part  due  to  errors 
and  is  certainly  affected  by  the  unequal  degree  of  superheating 
in  tests  3  and  5.  It  may  be  noted  that  the  actual  value  of  Qc  in 
calories  is  nearly  the  same  for  tests  i  and  2,  there  being  a  small 
apparent  increase  with  the  increase  of  cut-off,  which  is,  however, 
less  than  the  probable  error  of  the  tests.  The  exhaust  waste  Qc 
is  much  more  irregular  for  tests  3  to  7  for  superheated  steam. 
The  increase  from  81  to  87  B.T.U.  from  test  6  to  test  7  may 
•properly  be  attributed  to  a  less  degree  of  superheating;  the 
increase  from  66  to  81  B.T.U.  for  tests  5  and  6  is  due  to  longer 
cut-off  and  less  superheating;  finally,  the  steady  reduction  from 
75  to  66  B.T.U.  for  the  three  tests  3,  4,  and  5  is  probably  due  to 
the  rise  of  temperature  of  the  superheated  steam,  which  more 


222  INFLUENCE   OF   THE   CYLINDER   WALLS 

than  compensates  for  the  effect  of  lengthening  the  cut-off. 
Finally  in  test  8  the  exhaust  waste  is  practically  reduced  to 
zero  by  the  use  of  strongly  superheated  steam  in  a  non-con- 
densing engine;  this  shows  clearly  that  the  exhaust  waste  Qe  by 
itself  is  no  criterion  of  the  value  of  a  certain  method  of  using 
steam. 

Steam-jackets.  —  If  the  walls  of  the  cylinder  of  a  steam- 
engine  are  made  double,  and  if  the  space  between  the  walls  is 
filled  with  steam,  the  cylinder  is  said  to  be  steam- jacketed. 
Both  barrel  and  heads  may  be  jacketed,  or  the  barrel  only  may 
have  a  jacket;  less  frequently  the  heads  only  are  jacketed.  The 
principal  effect  of  a  steam-jacket  is  to  supply  heat  during  the 
vaporization  of  any  water  which  may  be  condensed  on  the 
cylinder  walls.  The  consequence  is  that  more  heat  is  returned 
to  the  steam  during  expansion  and  the  walls  are  hotter  at  the 
end  of  exhaust  than  would  be  the  case  for  an  un jacketed  engine. 
This  is  evident  from  a  comparison  of  tests  i  and  n  in  Table  V. 
In  test  i  only  a  small  part  of  the  heat  absorbed  during  admission 
is  returned  during  expansion,  and  by  far  the  larger  part  is  wasted 
during  exhaust.  In  test  u  the  heat  returned  during  expansion 
is  equal  to  two-thirds  that  absorbed  during  admission,  though  a 
part  of  this  heat  of  course  comes  from  the  jacket.  About  half 
as  much  is  wasted  during  exhaust  as  is  absorbed  during  admission. 
The  condensation  of  steam  is  thus  reduced  indirectly;  that  is, 
the  chilling  of  the  cylinder  during  expansion,  and  especially 
during  exhaust,  is  in  part  prevented  by  the  jacket,  and  conse- 
quently there  is  less  initial  condensation  and  less  exhaust  waste, 
and  in  general  a  gain  in  economy.  The  heat  supplied  during 
expansion,  though  it  does  some  work,  is  first  subjected  to  a 
loss  of  temperature  in  passing  from  the  steam  in  the  jacket  to 
the  cooler  water  on  the  walls  of  the  cylinder,  and  such  a  non- 
reversible  process  is  necessarily  accompanied  by  a  loss  of  effi- 
ciency. On  the  other  hand,  the  heat  supplied  by  a  jacket  during 
exhaust  passes  with  the  steam  directly  into  the  exhaust-pipe. 
It  appears,  then,  that  the  direct  effect  of  a  steam-jacket  is  to 
waste  heat;  the  indirect  effect  (drying  and  warming  the  cylinder) 


APPLICATION   TO   MULTIPLE-EXPANSION   ENGINES      223 

reduces  the  initial  condensation  and  the  exhaust  waste  and  often 
gives  a  notable  gain  in  economy. 

Application  to  Multiple-expansion  Engines.  —  The  application 
of  Hirn's  analysis  to  the  high- pressure  cylinder  of  a  compound  or 
multiple-expansion  engine  may  be  made  by  using  equations 
(159),  (160),  and  (162)  for  calculating  Qa,  Qb,  and  Qd,  while 
equation  (174)  may  be  used  to  find  Qc. 

A  similar  set  of  equations  may  be  written  for  the  next  cylinder, 
whether  it  be  the  low-pressure  cylinder  of  a  compound  engine 
or  the  intermediate  cylinder  of  a  triple  engine,  provided  we  can 
determine  the  value  of  Q',  the  heat  supplied  to  that  cylinder. 
But  of  the  heat  supplied  to  the  high-pressure  cylinder  a  part 
is  changed  into  work,  a  part  is  radiated,  and  a  part  is  rejected 
in  the  exhaust  waste.  The  heat  rejected  is  represented  by 

Q+Qj-AW  -Q. (175) 

where  Q  is  the  heat  supplied  by  the  steam  entering  the  cylinder, 
Qj  is  the  heat  supplied  by  the  jacket,  AW  is  the  heat-equivalent 
of  the  work  done  in  the  cylinder,  and  Qe  is  the  heat  radiated. 
Suppose  the  steam  from  the  high-pressure  cylinder  passes  to  an 
intermediate  receiver,  which  by  means  of  a  tubular  reheater  or 
by  other  means  supplies  the  heat  Qr,  while  there  is  an  external 
radiation  Qre.  The  heat  supplied  to  the  next  cylinder  is  con- 
sequently 

Q'  =  Q  +  Qj  -  AW  -  Qe  +  Qr  -  Qre    .    .  (176) 

In  a  like  manner  we  -may  find  the  heat  Q"  supplied  to  the 
next  cylinder;  for  example,  to  the  low-pressure  cylinder  of  a 
triple  engine. 

It  is  clear  that  such  an  application  of  Hirn's  analysis  can  be 
made  only  when  the  several  steam-jackets  on  the  high-  and  the 
low-pressure  cylinders,  and  the  reheater  of  the  receiver,  etc., 
can  be  drained  separately,  so  that  the  heat  supplied  to  each 
may  be  determined  individually. 

Table  VI  gives  applications  of  Hirn's  analysis  to  four  tests 
on  the  experimental  triple-expansion  engine  in  the  laboratory 
of  the  Massachusetts  Institute  of  Technology. 


224  INFLUENCE    OF   THE    CYLINDER   WALLS 

It  will  be  noted  that  the  steam  in  the  cylinders  becomes  drier 
in  its  course  through  the  engine,  under  the  influence  of  thorough 
steam-jacketing  with  steam  at  boiler-pressure,  and  is  practically 
dry  at  release  in  the  low-pressure  cylinder.  All  of  the  tests 
show  superheating  in  the  low-pressure  cylinder,  which  is  of 
course  possible,  for  the  steam  in  the  jackets  is  at  full  boiler- 
pressure  while  the  steam  in  the  cylinder  is  below  atmospheric 
pressure.  The  superheating  was  small  in  all  cases  —  not  more 
than  would  be  accounted  for  by  the  errors  of  the  tests.  The 
exhaust  waste  Qeff  from  the  low-pressure  cylinder  in  the  triple- 
expansion  tests  is  very  small  in  all  cases  —  less  than  two  per  cent 
of  the  heat  supplied  to  the  cylinders.  The  apparent  absurdity  of 
a  positive  value  for  Qe"  in  two  of  the  tests  (indicating  an  absorp- 
tion of  heat  by  the  cylinder  walls  during  exhaust)  may  properly 
be  attributed  to  the  unavoidable  errors  of  the  test. 

In  the  fourth  test,  when  the  engine  was  developing  120.3 
horse-power,  there  were  1305  pounds  of  steam  supplied  to  the 
cylinders  in  an  hour,  and  345  pounds  to  the  steam-jackets;  so 
that  the  steam  per  horse-power  per  hour  passing  through  the 
cylinders  was 

1305  -T-  120.3  =  10.86  pounds, 

while  the  condensation  in  the  jackets  was 

345  -T-  120.3  =  2-&7  pounds. 

So  that,  as  shown  on  page  145,  the  B.T.U.  per  horse-power  per 
minute  supplied  to  the  cylinders  by  the  entering  steam  was 
191.1,  while  the  jackets  supplied  40.6  B.T.U.,  making  in  all 
231.7  B.T.U.  per  horse-power  per  minute  for  the  heat-consumption 
of  the  engine.  In  the  same  connection  it  was  shown  that  the 
thermal  efficiency  of  the  engine  for  this  test  was  0.183,  while 
the  efficiency  for  incomplete  expansion  in  a  non-conducting 
cylinder  corresponding  to  the  conditions  of  the  test  was  0.222; 
so  that  the  engine  was  running  with  0.824  of  the  possible  efficiency. 
In  light  of  this  satisfactory  conclusion  some  facts  with  regard  to 
the  test  are  interesting. 


APPLICATION   OF   HIRN'S    ANALYSIS 


225 


TABLE  VI. 

APPLICATION  OF  HIRN'S  ANALYSIS  TO  THE  EXPERIMENTAL 
ENGINE  IN  THE  LABORATORY  OF  THE  MASSACHUSETTS 
INSTITUTE  OF  TECHNOLOGY. 

TRIPLE-EXPANSION;  CYLINDER  DIAMETERS,  9,  16,  AND  24  INCHES  ;    STROKE,  30 

•    INCHES. 

Trans.  Am.  Soc.  Mech.  Engrs.,  vol.  xii,  p.  740. 


I. 

II. 

III. 

IV. 

Duration  of  test   minutes              ... 

60 

60 

60 

60 

Total  number  of  revolutions    .... 
Revolutions  per  minute         

5299 
88.3 

5228 
87.1 

5J73 
86.2 

5148 
85.8 

Steam-consumption  during  test,  Ibs.  : 
Passing  through  cylinders     .... 
Condensation  in  h.p.  jacket      .    .    . 
in  first  receiver-jacket    .        ... 

"93 

g 

"57 

5° 
64 

1234 

29 
60 

I3°5 
3° 

72 

in  inter  jacket                    .... 

8c 

O2 

07 

IOC 

in  second  receiver-jacket  .... 

53 
80 

5° 
76 

52 

QO 

51 

Total 

id  78 

14.80 

IC7I 

i6co 

Condensing  water  for  test,  Ibs.     .    .    . 
Priming  by  calorimeter    

22847 
0.013 

22186 

O.OI2 

20244 
O.OII 

20252 

O    OI2 

Temperatures,  Fahrenheit: 
Condensed  steam  

OC.4 

O2  .  I 

102.4 

IOC.  7 

Condensing-water,  cold     
Condensing-water  hot 

41.9 

06.  1 

42.1 
06.6 

43-° 
106  •? 

42.8 
100  6 

Pressure   of  the   atmosphere,   by  the 
barometer,  Ibs  per  sq.  in  

14.8 

14.8 

14.  7 

14    7 

Boiler  pressure,  Ibs.  per  sq.  in.  abso- 
lute 

I  cr    •? 

I  CC     C 

i  c6  o 

IC7    7 

Vacuum  in  condenser,  inches  of  mer- 
curv 

2C    O 

2C.     I 

24.    I 

*!>/•/ 

23    O 

Events  of  the  stroke: 
High-pressure  cylinder  — 
Cut-off,  crank  end      

O.  IQ2 

o.  104 

O.  24C 

o  18* 

head  end 

O    21  C 

O   2OC 

O    271 

Release,  both  ends     

I.OO 

I  .OO 

I.OO 

U«3W3 

I    OO 

Compression,  crank  end  .... 
head  end                          .    . 

0.05 

o.oc 

0.05 
O  .  OC 

O.O4 
O   OC. 

0.04 
Ooc 

Intermediate  cylinder  — 
Cut-off,  both  ends      

O.  2O 

o.  20 

O    20 

o  20 

Release,  both  ends     

I.OO 

1  .00 

I    OO 

I    OO 

Compression,  crank  end   .... 
head  end 

0.03 
o  04 

0.03 

O    O4 

0.03 

o  04 

0.03 

Low-pressure  cylinder  — 
Cut-off  crank  end      .        .... 

0.18 

o.*8 

o  *8 

o  38 

head  end              

O.  3Q 

o.  7o 

O    3Q 

I.OO 

I.OO 

I    OO 

I    OO 

226 


INFLUENCE    OF   THE   CYLINDER   WALLS 


TABLE  VI  —  Continued. 


I. 

II. 

III. 

IV. 

Absolute  pressures     in  the  cylinder, 
pounds  per  sq.  in.  : 
High-pressure  cylinder  — 
Cut-off,  crank  end      .        ... 

14.1    O 

141    O 

138  8 

138    3 

head  end     

143    2 

143    I 

1  4O    3 

L6"'6 

140  6 

Release,  crank  end    

41    3 

41    1 

44    7 

48   4 

head  end 

41    1 

41    7 

4O    8 

Compression,  crank  end   .... 
head  end 

^A  -D 

43-7 

48    7 

45-3 

47    O 

48.5 

14    1 

53.2 

Admission,  crank  end 

64   1 

68  8 

O'l--  J 
72    2 

8l    2 

head  end      
Intermediate  cylinder  — 
Cut-off,  crank  end     .... 

75-3 

•77    2 

74-8 

37    6 

86.7 

38  6 

97.8 

4O   O 

head  end      

•2CT     O 

31    3 

30    6 

42    6 

Release,  crank  end     

13  6 

14    2 

14    7 

16  o 

head  end      

I  •?    4 

13  8 

14  0 

16.0 

Compression,  crank  end   .... 
head  end     
Admission,  crank  end 

2 

16.3 
17.9 

2O   4 

17-3 
18.8 
20  8 

18.2 

20.3 

22    2 

IQ.  0 

22.4 

23    I 

head  end     .            ... 

21    I 

22    8 

24    2 

26   7 

Low-pressure  cylinder  — 
Cut-off,  crank  end     

12    I 

12    6 

12    4 

13    2 

head  end     

12  .  0 

12    4 

13    I 

14.  O 

Release,  crank  end    

5.6 

5.  -l 

1-  I 

e.  7 

head  end 

5     A 

i  8 

5Q 

6   4 

Compression  and  admission  — 
crank  end 

37 

3    8 

41 

42 

head  end      .                ... 

43 

4tj 

4.6 

4.7 

Heat-equivalents    of    external  work, 
B.T.U.,  from  a  reason  indicator- 
diagram  to  line  of  absolute  vacuum  : 
High-pressure  cylinder  — 
During  admission, 
A  W&,  crank  end     ...'... 

c.  71 

1.78 

7.00 

8.19 

head  end 

6  61 

6   37 

842 

9.  IO 

During  expansion, 
A.  1V&  ,  crank  end     ...        . 

10  61 

10  76 

10.  40 

IO.  21 

head  end      

J.W.  VM) 

10.81 

II  .  04 

II  .  22 

II  .OO 

During  exhaust, 
A  We,  crank  end     

7.  73 

7.80 

8.44 

9.O2 

head  end 

8  08 

8  ii 

9    O4 

9.66 

During  compression, 
A  W&,  crank  end 

o  48 

o  60 

O  40 

o.  50 

head  end                 .... 

o.  62 

o.  64 

O.  73 

0.81 

Intermediate  cylinder  — 
During  admission, 
AW*',  crank  end    

7.18 

7.  C7 

7.98 

8.64 

head  end 

7   43 

7   cf 

8.46 

O.  IO 

During  expansion, 
AWS,  crank  end    

0.  14. 

0.  14 

O.OI 

10.  64 

head  end      

Q.22 

9.  31 

IO.  77 

II  .  14 

APPLICATION    OF    HIRN'S   ANALYSIS 

TABLE  VI  —  Continued. 


227 


I. 

II. 

III. 

IV. 

Intermediate  cylinder  — 
During  exhaust, 
AWe',  crank  end    

Q.27 

0.47 

9.  64 

10.54 

9.27 

9-47 

I0.l8 

10.84 

During  compression, 
AW  A    crank  end    

O    3Q 

O  43 

O.  C7 

0.4.6 

head  end      .        

o.  60 

o.  70 

0.78 

0.84 

Low-pressure  cylinder  — 
During  admission, 
AW+",  crank  end  

7.  7$ 

7.9ci 

8.77 

8.97 

head  end 

7OO 

8.iQ 

8  66 

93Q 

During  expansion, 
AWt>"y  crank  end 

6  8? 

7.  10 

6.86 

7   4? 

head  end      .    .        ... 

6.87 

7.  12 

7.  34 

7.87 

During  exhaust, 
AWe",  crank  end  

«;.o8 

<J.o8 

4.  62 

^.O9 

head  end      

<;.o8 

<.i6 

4.81 

tJ.OO 

During  compression, 
AW*",  crank  end 

o  oo 

o  oo 

O    OO 

o  oo 

head  end 

o  oo 

o.  oo 

o.oo 

o.  oo 

Quality  of  the  steam  in  the  cylinder. 
At  admission  and  at  compression 
the  steam  was  assumed  to  be  dry 
and  saturated: 
High-pressure  cylinder  — 
At  cut-off     .                               x. 

o  781; 

o  784 

o  848 

o  87? 

At  release    .                .    .          x2 

o  800 

O    QO3 

O.  Q2O 

O   Q3I 

Intermediate  cylinder  — 
At  cut-off    #,'  . 

0.899 

0.912 

0.906 

0.908 

At  release    xtf   . 
Low-pressure  cylinder  — 
At  cut-off     Xi"  . 

0.994 

,  J-978 

*  *  * 

c    *°i7° 

*    *'l74 

At  release    x2'f  . 
Interchanges    of    heat    between    the 
steam  and  the  walls  of  the  cylin- 
ders,   in    B.    T.    u.      Quantities 
affected  by  the  positive  sign  are 
absorbed  by  the   cylinder  walls; 
quantities  affected  by  the  negative 
sign  are  yielded  by  the  walls:  .    . 
High-pressure  cylinder  — 
Brought  in  by  steam      .   Q  .    .    . 
During  admission  .    .    .   QA     .    . 
During  expansion              Qt 

132.93 
23-54 
—  18  69 

130.77 
23-43 

—  10  28 

141.  II 

17.49 
—  I  <»    11 

149.84 

14-93 
—  Id.    O7 

—  8  16 

—     7    22 

L3-  66 

—      •}     CQ 

—    2    78 

During  compression  .    .   Q*     .    . 
Supplied  by  jacket     .    .    Q/     .    . 
Lost  by  radiation  .    .    .    Qt 
First  intermediate  receiver  — 
Supplied  by  jacket     .    .   Qr     .    . 
Lost  by  radiation  .    .    .   Q^    .  ^  . 

0-45 
4-56 
1.50 

4.92 
0.58 

0.51 
4.08 
1.52 

5.20 
0.58 

0.49 
2-39 

i-54 

5-67 

0.59 

*«J° 

0.52 
2.50 
1.54 

5-95 

0.5-) 

*  Superheated. 


228 


INFLUENCE   OF   THE    CYLINDER   WALLS 


TABLE  VI  —  Continued. 


I. 

II. 

III. 

IV. 

Intermediate  cylinder  — 

Brought  in  by  steam      .   Q'     .    . 

131.89 

129.61 

137-87 

146.64 

During  admission  .    .    .    Q*'    .    . 

13.62 

11.74 

"•33 

11.75 

During  expansion      .    .    Obr 

—  18.65 

—  18  84. 

—  20.  30 

—  21.88 

During  exhaust  .    .    .    .    Q,'    .    . 

O.22 

A  <-*  .  U£+ 

2.88 

During  compression  .    .    Q*'    .    . 

0.44 

0.5I 

0.62 

o-59 

Supplied  by  jacket     .    .   Q/    .    . 

6.82 

7-5° 

7-97 

8.64 

Lost  by  radiation  .    .    .   Q/   .    . 

2.45 

2.48 

2.50 

2-51 

Second  intermediate  receiver— 

Supplied  by  jacket     .    .   Q/    .    . 

4.20 

4.04 

4.27 

4.22 

Lost  by  radiation   .    .    .    QrS  .    . 

1.20 

1.22 

1.23 

1.24 

Low-pressure  cylinder  — 

Brought  in  by  steam     .   Q"     .    . 

132.14 

I30-50 

138.61 

J47-33 

During  admission  .    .    .   Q&"  .    . 

5.85 

3-°5 

5-57 

5-29 

During  expansion  .    .    .   Qt>"  .    . 

-  9-51 

-   7-°9 

-  8.65 

—  10.13 

During  exhaust  ....   Qe"  .    . 

2-53 

2.23 

-    1-44 

-   o.n 

During  compression  .    .   Qj'  .    . 

o.oo 

0.00 

0.00 

o.oo 

Supplied  by  jacket     .    .   Q/"  .    . 

7.08 

6.20 

7.41 

7-i4 

Lost  by  radiation  .    .    .   Q,"  .    . 

4-34 

4.40 

4-45 

4-47 

Total  loss  by  radiation  — 

By  preliminary  tests  .    .    SQ.  .    . 

10.07 

IO.2O 

10.31 

IO-35 

By  equation  (171)  

11.68 

10.  19 

8.75 

8.07 

Power  and  economy: 

/  0 

Heat-equivalents     of     works      per 

stroke  — 

H.  P.  cylinder     .    .    .    .  AW  .    . 

8.44 

8.34 

9.17 

9-S2 

Interm.  cylinder.    .    .    .   AW     . 

7.12 

6.95 

7-77 

8.42 

L.P.  cylinder      .    .    .    .AW"    . 

9.64 

io.  06 

10.87 

11.79 

Totals 

2  5  .  20 

2  C     -if 

27.81 

2 

Total  heat  furnished  by  jackets  .    . 

27.58 

*0  •  O  0 

27.02 

27.71 

28.45 

Distribution  of  work  — 

High-pressure  cylinder  

i  .00 

I.OO 

I  .  OO 

I  .  OO 

Intermediate  cylinder    

0.84 

0.83 

0.88 

Low-pressure  cylinder 

i  .  14 

o 

1*21 

I    IO 

i  .  24. 

Horse-power 

104.  o 

IO4.    2 

i  .  j.y 
T  I  •?     I 

Steam  per  H  P   per  hour 

J.  w-J.  .  y 

14.  6? 

*w*f  •  ^ 

J.  ij  .   i 

1  3    73 

B.T.U.  per  H.P.  per  minute     .    .    . 

**r*  "3 

247 

241 

236'9< 

ij  '  1  o 
232 

It  will  be  noted  that  for  test  IV  149.84  B.T.U.  per  stroke  are 
brought  in  by  the  steam  supplied  to  the  high-pressure  cylinder 
and  that  28.45  B.T.U.  per  stroke  are  supplied  by  the  steam-jackets; 
and  that,  further,  29.73  B.T.U.  are  changed  into  work  while  10.35 
are  radiated.  Thus  it  appears  that  the  jackets  furnished  almost 
as  much  heat  as  was  required  to  do  all  the  work  developed.  Of 
the  heat  furnished  by  the  jackets  something  more  than  a  third 


QUALITY    OF    STEAM   AT    COMPRESSION  229 

was  radiated;  the  other  two-thirds  may  fairly  be  considered 
to  have  been  changed  into  work,  since  the  exhaust  waste  of  the 
low-pressure  cylinder  was  practically  zero. 

Quality  of  Steam  at  Compression.  —  In  all  the  work  of  this 
chapter  the  steam  in  the  cylinder  at  compression  has  been  con- 
sidered to  be  dry  and  saturated,  and  it  has  been  asserted  that 
little  if  any  error  can  arise  from  this  assumption.  It  is  clear 
that  some  justification  for  such  an  assumption  is  needed,  for  a 
relatively  large  weight  of  water  in  the  cylinder  would  occupy 
a  small  volume  and  might  well  be  found  adhering  to  the  cylinder 
walls  in  the  form  of  a  film  or  in  drops;  such  a  weight  of  water 
would  entirely  change  our  calculations  of  the  interchanges  of 
heat.  The  only  valid  objection  to  Hirn's  analysis  is  directed 
against  the  assumption  of  dry  steam  at  compression.  Indeed, 
when  the  analysis  was  first  presented  some  critics  asserted  that 
the  assumption  of  a  proper  amount  of  water  in  the  cylinder  is 
all  that  is  required  to  reduce  the  calculated  interchanges  of  heat 
to  zero.  It  is  not  difficult  to  refute  such  an  assertion  from 
almost  any  set  of  analyses,  but  unfortunately  such  a  refutation 
cannot  be  made  to  show  conclusively  that  there  is  little  or  no 
water  in  the  cylinder  at  compression;  in  every  case  it  will  show 
only  that  there  must  be  a  considerable  interchange  of  heat. 

For  the  several  tests  on  the  Hirn  engine  given  in  Table  V, 
Hallauer  determined  the  amount  of  moisture  in  the  steam  in  the 
exhaust-pipe,  and  found  it  to  vary  from  3  to  10  per  cent.  Professor 
Carpenter  *  says  that  the  steam  exhausted  from  the  high-pressure 
cylinder  of  a  compound  engine  showed  12  to  14  per  cent  of 
moisture.  Numerous  tests  made  in  the  laboratory  of  the 
Massachusetts  Institute  of  Technology  show  there  is  never  a 
large  percentage  of  water  in  exhaust-steam.  Finally,  such  a 
conclusion  is  evident  from  ordinary  observation.  Starting  from 
this  fact  and  assuming  that  the  steam  in  the  cylinder  at  com- 
pression is  at  least  as  dry  as  the  steam  in  the  exhaust-pipe,  we 
are  easily  led  to  the  conclusion  that  our  assumption  of  dry  steam 
is  proper.  Professor  Carpenter  reports  also  that  a  calorimeter 

*  Trans.  Am.  Soc.  Mech.  Engrs.,  vol.  xii,  p.  811. 


230  INFLUENCE    OF   THE    CYLINDER    WALLS 

test  of  steam  drawn  from  the  cylinder  during  compression 
showed  little  or  no  moisture.  Nevertheless,  there  would  still 
remain  some  doubt  whether  the  assumption  of  dry  steam  at 
compression  is  really  justified,  were  we  not  so  fortunate  as  to 
have  direct  experimental  knowledge  of  the  fluctuations  of  tem- 
perature in  the  cylinder  walls. 

Dr.  Hall's  Investigations.  —  For  the  purpose  of  studying 
the  temperatures  of  the  cylinder  walls  Dr.  E.  H.  Hall  used  a 
thermo-electric  couple,  represented  by  Fig.  56.  /  is  a  cast- 
iron  plug  about  three-quar- 
ters of  an  inch  in  diameter, 
which  could  be  screwed  into 
the  hole  provided  for  attach- 

FIG.  56.  .     , . 

mg  an  indicator-cock  to  the 

cylinder  of  a  steam-engine.  The  inner  end  of  the  plug 
carried  a  thin  cast-iron  disk,  which  was  assumed  to  act  as 
a  part  of  the  cylinder  wall  when  the  plug  was  in  place.  To 
study  the  temperature  of  the  outside  surface  of  the  disk  a  nickel 
rod  N  was  soldered  to  it,  making  a  thermo-electric  couple. 
Wires  from  /  and  N  led  to  another  couple  made  by  soldering 
together  cast-iron  and  nickel,  and  this  second  couple  was  placed 
in  a  bath  of  paraffine  which  could  be  maintained  at  any  desired 
temperature.  In  the  electric  circuit  formed  by  the  wires  joining 
the  two  thermo-electric  couples  there  was  placed  a  galvanometer 
and  a  circuit-breaker.  The  circuit-breaker  was  closed  by  a 
cam  on  the  crank-shaft,  which  could  be  set  to  act  at  any  point 
of  the  revolution.  If  the  temperature  of  the  outside  of  the  disk 
S  differed  from  the  temperature  of  the  paraffine  bath  at  the  instant 
when  contact  was  made  by  the  cam,  a  current  passed  through 
the  wires  and  was  indicated  by  the  galvanometer.  By  properly 
regulating  the  temperature  of  the  bath,  the  current  could  be 
reduced  and  made  to  cease,  and  then  a  thermometer  in  the  bath 
gave  the  temperature  at  the  surface  of  the  disk  for  the  instant 
when  the  cam  closed  the  electric  circuit.  Two  points  in  the 
steam-cycle  were  chosen  for  investigation,  one  immediately 
after  cut-off  and  the  other  immediately  after  compression,  since 


CALLENDAR   AND   NICOLSON'S    INVESTIGATIONS         231 

they  gave  the  means  of  investigating  the  heat  absorbed  during 
compression  and  admission  of  steam,  and  the  heat  given  up 
during  expansion  and  exhaust. 

Three  different  disks  were  used :  the  first  one  half  a  millimetre 
thick,  the  second  one  millimetre  thick,  and  a  third  two  milli- 
metres thick.  From  the  fluctuations  of  temperature  at  these 
distances  from  the  inside  surface  of  the  wall  some  idea  could  be 
obtained  concerning  the  variations  of  temperature  at  the  inner 
surface  of  the  cylinder,  and  also  how  far  the  heating  and  cooling 
of  the  walls  extended. 

The  account  given  here  is  intended  only  to  show  the  general 
idea  of  the  method,  and  does  not  adequately  indicate  the  labor 
difficulties  of  the  investigation  which  involved  many  secondary 
investigations,  such  as  the  determination  of  the  conductivity  of 
nickel.  Having  shown  conclusively  that  there  is  an  energetic 
action  of  the  walls  of  the  cylinder,  Dr.  Hall  was  unable  to  continue 
his  investigations. 

Callendar  and  Nicolson's  Investigations.  —  A  very  refined 
and  complete  investigation  of  the  temperature  of  the  cylinder 
walls  and  also  of  the  steam  in  the  cylinder  was  made  by 
Callendar  and  Nicolson  *  in  1895  at  the  McGill  University, 
by  the  thermo-electric  method. 

The  wall  temperatures  were  determined  by  a  thermo-electric 
couple  of  which  the  cylinder  itself  was  one  element  and  a  wrought- 
iron  wire  was  the  other  element.  To  make  such  a  couple,  the 
cylinder  wall  was  drilled  nearly  through,  and  the  wire  was 
soldered  to  the  bottom  of  the  hole.  Eight  such  couples  were 
established  in  the  cylinder-head,  the  thickness  of  the  unbroken 
wall  varying  from  o.oi  of  an  inch  to  0.64  of  an  inch.  Four  pairs 
of  couples  were  established  along  the  cylinder-barrel,  one  near 
the  head,  and  the  others  at  4  inches,  6  inches,  and  12  inches 
from  the  head.  One  of  each  pair  of  wall  couples  was  bored  to 
within  0.04  of  an  inch,  and  the  other  to  0.5  of  an  inch  of  the 
inside  surface  of  the  cylinder.  Other  couples  were  established 
along  the  side  of  the  cylinder  to  study  the  flow  of  heat  from  the 

*  Proceedings  of  the  Inst.  Civ,  Engrs.,  vol.  cxxxii. 


INFLUENCE   OF   THE   CYLINDER    WALLS 


head  toward  the  crank  end.  The  temperature  of  the  steam 
near  the  cylinder-head  was  measured  by  a  platinum  thermometer 
capable  of  indicating  correctly  rapid  fluctuations  of  temperature. 

The  engine  used  for  the  investigations  was  a  high-speed 
engine,  with  a  balanced  slide-valve  controlled  by  a  fly-wheel 
governor.  During  the  investigations  the  cut-off  was  set  at  a 
fixed  point  (about  one-fifth  stroke),  and  the  speed  was  controlled 
externally.  By  the  addition  of  a  sufficient  amount  of  lap  to 
prevent  the  valve  from  taking  steam  at  the  crank  end  the  engine 
was  made  single-acting.  The  normal  speed  of  the  engine  was 
250  revolutions  per  minute,  but  during  the  investigations  the  speed 
was  from  40  to  90  revolutions  per  minute.  The  diameter  of  the 
cylinder  was  10.5  inches  and  the  stroke  of  the  piston  was  12 
inches.  The  clearance  was  ten  per  cent  of  the  piston  displacement. 

From  the  indicator-diagrams  an  analysis,  nearly  equivalent  to 
Hirn's  analysis,  showed  the  heat  yielded  to  or  taken  from  the 
walls  by  the  steam;  on  the  other  hand  the  thermal  measurements 
gave  an  indication  of  the  heat  gained  by  or  yielded  by  the  walls. 
The  results  are  given  in  the  following  table;  and  considering  the 
difficulty  of  the  investigation  and  the  large  allowance  for  leakage, 
the  concordance  must  be  admitted  to  be  very  satisfactory. 

TABLE  VII. 

INFLUENCE  OF  THE  WALLS  OF  THE  CYLINDER. 

CALLENDAR  AND  NICOLSON,  Proc.  Inst.  Civ.  Engrs.,  1897. 


I. 

II. 

III. 

IV. 

V. 

VI. 

VII. 

Duration,  minutes    

37 

68 

55 

79 

76 

35 

25 

Revolutions  per  minute   .    .    . 

43-8 

45-7 

47-7 

70.4 

73-4 

81.7 

97.0 

Mean  gauge-pressure   .... 

87.9 

89.2 

94.4 

98.1 

92.0 

94-2 

96.0 

Gross  steam  per  revolution  .    . 

o.  1422 

0.1437 

0.1483 

0.1094 

0.1036 

O.  IOOO 

0.0856 

Leakage  correction  

0.1004 

0.0976 

0.0990 

0.0697 

0.0627 

0.0576 

0.0494 

Net  steam  per  revolution    .    . 
Steam  caught  at  compression 
Weight  of  mixture  in  cylinder 
Indicated  steam  at  quarter  stroke 
Indicated  steam  at  release  .    . 

0.0418 
•0.0107 
0.0525 
0.0407 
o  .  0466 

0.0461 
0.0104 
0.0565 
0.0414 
0.0456 

0.0493 
0.0103 
0.0596 
0.0437 
0.0488 

0.0397 
0.0099 
o  .  0496 
0.0418 
o  .  0460 

o  .  0409 
o  .  0098 
0.0507 
0.0394 
0.0436 

0.0424 

0.0100 

0.0524 

o  .  0408 

0.0454 

0.0362 
0.0105 
o  .  0467 
0.0393 
0.0426 

Increase  of  indicated  weight   . 

0.0059 

0.0042 

0.0051 

0.0042 

o  .  0042 

o  .  0046 

0.0033 

Adiabatic  condensation    .    .    . 

0.0019 

0.0020 

0.0021 

0.0020 

0.0019 

0.0020 

0.0019 

Indicated  evaporation  .... 

0.0078 

O.OO62 

O.OO72 

o  .  0062 

0.0061 

0.0066 

0.0052 

Calculated  evaporation    .    .    . 
Indicated  condensation    .    .    . 

0.0076 
0.0118 

0.0073 
O.OI5I 

0.0072 
0.0159 

0.0048 
0.0078 

o  .  0046 
0.0113 

0.0041 
0.0116 

0.0035 

0.0074 

Calculated  condensation  .    .    . 

0.0148 

0.0142 

0.0136 

o  .  0092 

0.0089 

0.0080 

0.0067 

Indicated  horse-power     .... 

4.10 

4-34 

4.78 

7.02 

6.67 

7.71 

8.81 

Steam  per  H.P.  per  hour,  pounds 

26.8 

29.1 

29-5 

23.8 

27.1 

26.  9 

23.8 

CALLENDAR   AND    NICOLSON'S    INVESTIGATIONS         233 

The  platinum  thermometer  near  the  cylinder-head  showed 
superheating  throughout  compression,  thus  confirming  our  idea 
that  steam  can  be  treated  as  dry  and  saturated  at  the  beginning 
of  compression.  This  same  thermometer  fell  rapidly  during 
admission  and  showed  saturation  practically  up  to  cut-off,  as 
of  course  it  should;  after  cut-off  it  began  again  to  show  a  tem- 
perature higher  than  that  due  to  the  indicated  pressure,  which 
shows  that  the  cylinder-head  probably  evaporated  all  the  moisture 
from  its  surface  soon  after  cut-off.  If  this  conclusion  is  correct, 
there  would  appear  to  be  little  advantage  from  steam-jacketing 
a  cylinder-head,  a  conclusion  which  is  borne  out  by  tests  on  the 
experimental  engine  at  the  Massachusetts  Institute  of  Technology. 

The  following  table  gives  the  areas,  temperatures,  and  the  heat 
absorbed  during  a  given  test  by  the  various  surfaces  exposed  to 
steam  at  the  end  of  the  stroke,  i.e.,  the  clearance  surface. 


TABLE  VIII. 

CYCLICAL  HEAT-ABSORPTION   FOR   CLEARANCE   SURFACES. 


Portions  of  surface  considered. 

Area 
of  surface, 
square  feet. 

Mean 
temperature, 
F. 

Heat  absorbed 
B.T.U. 
per  minute. 

Cover  face,  10.5  inches  diameter      .    . 
Cover  side    3  o  inches         .            ... 

O.6o 

o  70 

3°5 
30? 

68 
7Q 

Piston  face,  10.5  inches  diameter.    .    . 
Piston  side,  o.t;  inch  

0.60 

O.  II 

295 

2Q£ 

no 

20 

Barrel  side,  3.0  inches    

o.  71 

2Q7 

123 

Counterbore,  0.5  inch     . 
Ports  and  valves 

0.  12 
O    QO 

29I 

•7QC 

28 

1  02 

Sums  and  means     

7.  74 

?OI 

e-jQ 

The  heat  absorbed  by  the  side  of  the  cylinder  wall  uncovered 
by  the  piston  up  to  0.25  of  the  stroke  was  estimated  to  be  55 
B.T.U.  per  minute,  which  added  to  the  above  sum  gives  585  B.T.U.  ; 
from  which  it  appears  that  90  per  cent  of  the  condensation  is 
chargeable  to  the  clearance  surfaces,  which  were  exceptionally 
large  for  this  type  of  engine.  Further  inspection  shows  that 
the  condensation  on  the  piston  and  the  barrel  is  much  more 


234  INFLUENCE    OF   THE   CYLINDER   WALLS 

energetic  than  on  the  cover  or  head.  For  example,  the  face  of 
the  piston  absorbs  no  B.T.U.,  while  the  face  of  the  cover  absorbs 
only  68  B.T.U.,  and  the  sides  of  the  cover  and  of  the  barrel,  each 
3  inches  long,  absorb  79  and  123  B.T.U.  respectively.  This 
relatively  small  action  of  the  surface  of  the  head  indicates  in 
another  form  that  less  gain  is  to  be  anticipated  from  the  appli- 
cation of  a  steam-jacket  to  the  head  than  to  the  barrel  of  a 
steam-engine. 

The  exposed  surfaces  at  the  side  of  the  cylinder-head  and 
the  corresponding  side  of  the  barrel  are  due  to  the  use  of  a 
deeply  cored  head  which  protrudes  three  inches  into  the  counter- 
bore  of  the  cylinder,  and  which  has  the  steam-tight  joint  at  the 
flange  of  the  head.  It  would  appear  from  this  that  a  notable 
reduction  of  condensation  could  be  obtained  by  the  simple  expe- 
dient of  making  a  thin  cylinder-head. 

Leakage  of  Valves.  — Preliminary  tests  when  the  engine  was 
at  rest  showed  that  the  valve  and  piston  were  tight.  The  valve 
was  further  tested  by  running  it  by  an  electric  motor  when  the 
piston  was  blocked,  the  stroke  of  the  valve  being  regulated  so 
that  it  did  not  quite  open  the  port,  whereupon  it  appeared  that 
there  was  a  perceptible  but  not  an  important  leak  past  the  valve 
into  the  cylinder.  There  was  also  found  to  be  a  small  leakage 
past  the  piston  from  the  head  to  the  crank  end. 

But  the  most  unexpected  result  was  the  large  amount  of  leakage 
past  the  valve  from  the  steam-chest  into  the  exhaust.  This  was 
determined  by  blocking  up  the  ports  with  lead  and  running  the 
valve  in  the  normal  manner  by  an  electric  motor.  This  leak- 
age appeared  to  be  proportional  to  the  difference  of  pressure 
causing  the  leak,  and  to  be  independent  of  the  number  of 
reciprocations  of  the  valve  per  minute.  From  the  tests  thus 
made  on  the  leakage  to  the  exhaust,  the  leakage  correction  in 
Table  VII  was  estimated.  Although  the  investigators  concluded 
that  their  experimental  rate  of  leakage  was  quite  definite,  it 
would  appear  that  much  of  the  discrepancy  between  the  indicated 
and  calculated  condensation  and  vaporization  can  be  attributed 
to  this  correction,  which  was  two  or  three  times  as  large  as  the 


LEAKAGE    OF   VALVES  235 

weight  of  steam  passing  through  the  cylinder.  Under  the  most 
favorable  condition  (for  the  seventh  test)  the  leakage  was 
0.0494  of  a  pound  per  stroke,  and  since  there  were  97  strokes 
per  minute,  it  amounted  to 

0.0494  X  97  X  60  =  287.5 

pounds  per  hour,  or  32.6  pounds  per  horse-power  per  hour,  so 
that  the  steam  supplied  per  horse-power  per  hour  amounted  to 
56.4  pounds.  If  it  be  assumed  that  the  horse-power  is  propor- 
tional to  the  number  of  revolutions,  then  the  engine  running 
double-acting  will  develop  about  44  horse-power,  and  the  leak- 
age then  would  be  reduced  to  6.5  pounds  per  horse-power 
per  hour.  Such  a  leakage  would  have  the  effect  of  increas- 
ing the  steam-consumption  from  23.5  to  30  pounds  of  steam  per 
horse-power  per  hour. 

To  substantiate  the  conclusions  just  given  concerning  the 
leakage  to  the  exhaust,  the  investigators  made  similar  tests  on 
the  leakage  of  the  valves  of  a  quadruple- expansion  engine,  which 
had  plain  unbalanced  slide-valves.  The  valves  chosen  were  the 
largest  and  smallest;  both  were  in  good  condition,  the  largest 
being  absolutely  tight  when  at  rest.  Allowing  for  the  size  and 
form  of  the  valve  and  for  the  pressure,  substantially  identical 
results  were  obtained. 

The  following  provisional  equation  is  proposed  for  calculat- 
ing the  leakage  to  the  exhaust  for  slide-valves: 

kep 

leakage  =  — -*-> 
I 

where  /  is  the  lap  and  e  is  the  perimeter  of  the  valve,  both  in 
inches,  and  p  is  the  pressure  in  pounds  in  the  steam-chest  in 
excess  of  the  exhaust-pressure.  The  value  of  the  constant 
in  the  above  equation  is  0.021  for  the  high-speed  engine  used  by 
Callendar  and  Nicolson,  and  is  0.019  f°r  one  test  each  of  the 
valves  for  the  quadruple  engine,  while  another  test  on  the  large 
valve  gave  0.021. 


236  INFLUENCE    OF   THE   CYLINDER   WALLS 

This  matter  of  the  leakage  to  the  exhaust  is  worthy  of  further 
investigation.  Should  it  be  found  to  apply  in  general  to  slide- 
valve  and  piston- valve  engines  it  would  go  far  towards  explaining 
the  superior  economy  of  engines  with  separate  admission-  and 
exhaust-valves,  and  especially  of  engines  with  automatic  drop- 
cut-off  valves  which  are  practically  at  rest  when  closed.  It 
may  be  remarked  that  the  excessive  leakage  for  the  engine 
tested  appears  to  be  due  to  the  size  and  form  of  valves.  The 
valve  was  large  so  as  to  give  a  good  port-opening  when  the  cut-off 
was  shortened  by  the  fly-wheel  governor,  and  was  faced  off  on 
both  sides  so  that  it  could  slide  between  the  valve-seat  and  a 
massive  cover-plate.  The  cover-plate  was  recessed  opposite 
the  steam-ports,  and  the  valve  was  constructed  so  as  to  admit 
steam  at  both  faces;  from  one  the  steam  passed  directly  into  the 
cylinder,  and  from  the  other  it  passed  into  the  cover-plate  and 
thence  into  the  steam-port.  This  type  of  valve  has  long  been 
used  on  the  Porter- Allen  and  the  Straight-line  engines;  the  former, 
however,  has  separate  steam-  and  exhaust- valves.  Such  a  valve 
has  a  very  long  perimeter  which  accounts  for  the  very  large  effect 
of  the  leakage. 

Callendar  and  Nicolson  consider  that  the  leakage  is  probably 
in  the  form  of  water  which  is  formed  by  condensation  of  steam 
on  the  surface  of  the  valve-seat  uncovered  by  the  valve,  and  say 
further,  that  it  is  modified  by  the  condition  of  lubrication  of 
the  valve-seat,  as  oil  hinders  the  leakage. 


CHAPTER  XII. 

ECONOMY  OF  STEAM-ENGINES. 

IN  this  chapter  an  attempt  is  made  to  give  an  idea  of  the 
economy  to  be  expected  from  various  types  of  steam-engines 
and  the  effects  of  the  various  means  that  are  employed  when 
the  best  performance  is  desired. 

Table  X  gives  the  economy  of  various  types  of  engines,  and 
represents  the  present  state  of  the  art  of  steam-engine  construc- 
tion. It  must  be  considered  that  in  general  the  various  engines 
for  which  results  are  given  in  the  table  were  carefully  worked  up 
to  their  best  performance  when  these  tests  were  made.  In 
ordinary  service  these  engines  under  favorable  conditions  may 
consume  five  or  ten  per  cent  more  steam  or  heat ;  under  unfavor- 
able conditions  the  consumption  may  be  half  again  or  twice  as 
much. 

All  the  examples  in  the  table  are  taken  from  reliable  tests;  a 
few  of  these  tests  are  stated  at  length  in  the  chapter  on  the  influ- 
ence of  the  cylinder  walls;  others  are  taken  from  various  series 
of  tests  which  will  be  quoted  in  connection  with  the  discussion 
of  the  effects  of  such  conditions  as  steam-jacketing  and  com- 
pounding; the  remaining  tests  will  be  given  here,  together  with 
some  description  of  the  engines  on  which  the  tests  were  made. 
These  tables  of  details  are  to  be  consulted  in  case  fuller  informa- 
tion concerning  particular  tests  is  desired. 

The  first  engine  named  in  the  table  is  at  the  Chestnut  Hill 
pumping-station  for  the  city  of  Boston.  Its  performance  is 
the  best  known  to  the  writer  for  engines  using  saturated  steam. 
Some  engines  using  superheated  steam  have  a  notably  less  steam- 
consumption  ;  but  the  heat-consumption,  which  is  a  better  criterion 
of  engine  performance  for  such  tests,  is  little  if  any  better.  The 
first  compound  engine  for  which  results  are  given,  used  9.6 

237 


238 


ECONOMY    OF   STEAM-ENGINES 


TABLE  X. 

EXAMPLES   OF   STEAM-ENGINE   ECONOMY. 


Type  of  Engine. 

Revolutions 
per  minute. 

Steam-pressure. 
Pounds  per 
square  inch. 

Horse-power. 

Steam  per  horse- 
power per  hour. 
Pounds. 

B.T.U.  per 
horse-power 
per  min. 

Coal  per  horse- 
power per  hour. 
Pounds. 

Triple-expansion  engines  : 
Leavitt  pumping-engine   at  Chestnut  Hill 
Sulzer  mill-engine  at  Augsburg    
Experimental  engine  at  the  Massachusetts 
Institute  of  Technology    

50.6 
56 

t>2 

I76 
149 

576 

1823 

11.2 

n-3 

204 

I-I5 
I.I9 

Marine  engine  Inn&       .    .        . 

y^ 
61 

*4y 

76- 

I25 

A,  c 

J3-7 

231 

T      Aft 

Marine  engine  Meteor       

72 

IOD 

°45 

13-4 

•    .    • 

M^arine  engine  BTookline  

1* 

i"*D 

1994 

15.0 

26? 

Compound  engines: 
Horizontal  mill  -engine  : 
superheated 

128 

*5'T 

*5'3 

n    fi 

*  }o 

saturated 

J35 

IJ5 

9.  u 

TT     8 

1  99 

Leavitt  pumping-engine  at  Louisville     .    . 
M^arine  engine  Rush          

ll£  I 

18.6 

71 

J35 
J37 
60 

127 

643 
266 

12.2 

18  A 

213 

222 

M^arine  engine  Fusi  Yama  

s6 

uy 

C7 

^•45 
2  66 

Simple  engines,  condensing: 
Corliss  engine  at  Creusot 

60 

J  i 
8, 

o/1 

T7fi 

Corliss  engine  without  jacket  

rn 

°4 
61 

170 

I  <O 

18  i 

"    "    * 

Harris-  Corliss  engine  at  Cincinnati     .    .    . 
[Marine  engine  Gdllatin 

76 

96 
6c 

Aow 
145 
260 

19.4 

Simple  engines,  non-condensing: 
Corliss  engine  at  Creusot 

J-1 
6l 

uj 

Corliss  engine  without  jacket 

61 

78 

^61 

"  O 

Harris-Corliss  engine  at  Cincinnati     .    .    . 
Harris-Corliss  engine  at  the  Massachusetts 
Institute  of  Technology    

76 
61 

96 

77 

I2O 

16 

23-9 

•?  •?      C 

1*8 

... 

Direct-acting  steam-pumps: 
Fire-pump  at  the  Massachusetts  Institute 
of  Technologv 

*oo 

d.7 

67 

at  reduced  power 

*ro 

PQ 

6  8 

12? 

2070 

Steam-  and  feed-pump  on  the  Minneapolis 
at  reduced  power       

41 

*2    6 

8.8 
i  6 

A^0 

91 
247 

pounds  of  steam  and  199  B.T.U.  per  minute,  the  gain  being 
hardly  more  than  the  variation  that  might  be  attributed  to  differ- 
ence in  apparatus,  etc.  The  Chestnut  Hill  engine,  which  was  de- 


*  Strokes  per  minute. 


TRIPLE-EXPANSION    LEAVITT    PUMPING-ENGINE          239 

signed  by  Mr.  E.  D.  Leavitt,  has  three  vertical  cylinders  with  their 
pistons  connected  to  cranks  at  120°.  Each  cylinder  has  four 
gridiron  valves,  each  valve  being  actuated  by  its  own  cam  on  a 
common  cam-shaft;  the  cut-off  for  the  high-pressure  cylinder  is 
controlled  by  a  governor.  Steam-jackets  are  applied  to  the 
heads  and  barrels  of  each  cylinder,  and  tubular  reheaters  are 
placed  between  the  cylinders.  Steam  at  boiler-pressure  is  sup- 
plied to  all  the  jackets  and  to  the  tubular  reheaters. 


TABLE  XL 

TRIPLE-EXPANSION   LEAVITT   PUMPING-ENGINE  AT  THE 
CHESTNUT  HILL  STATION,   BOSTON,   MASSACHUSETTS. 

CYLINDER   DIAMETERS    13.7,    24.375,    AND   39    INCHES;    STROKE   6   FEET. 

By  Professor  E.  F.  MILLER,  Technology  Quarterly,  vol.  ix,  p.  72. 

Duration,  hours 24 

Total  expansion 21 

Revolutions  per  minute 50.6 

Steam-pressure  above  atmosphere,  pounds  per  square  inch *75'7 

Barometer,  pounds  per  square  inch 14.9 

Vacuum  in  condenser,  inches  of  mercury 27-2S 

Pressure  in  high  and  intermediate  jacket  and  reheaters,  pounds  per 

square  inch *75-7 

Pressure  in  low-pressure  jacket,  pounds  per  square  inch 99 . 6 

Horse-power 575-7 

Steam  per  horse-power  per  hour,  pounds  . 11.2 

Thermal  units  per  horse-power  per  minute 204.3 

Thermal  efficiency  of  engine,  per  cent 20.8 

Efficiency  for  non-conducting  engine,  per  cent 28.0 

Ratio  of  efficiencies,  per  cent 74 

Coal  per  horse-power  per  hour,  pounds 1.146 

Duty  per  1,000,000  B.T.U 141,855,000 

Efficiency  of  mechanism,  per  cent  ....  89 . 5 


The  Sulzer  engine  at  Augsburg  has  four  cylinders  in  all,  a  high- 
pressure,  an  intermediate,  and  two  low-pressure  cylinders.  The 
high-pressure  cylinder  and  one  low-pressure  cylinder  are  in  line, 
with  their  pistons  on  one  continuous  rod,  and  the  intermediate 


240 


ECONOMY  OF   STEAM-ENGINES 


cylinder  is  arranged  in  a  similar  way  with  the  other  low-pressure 
cylinder.  The  engine  has  two  cranks  at  right  angles,  between 
which  is  the  fly-wheel,  grooved  for  rope-driving.  Each  cylinder 
has  four  double-acting  poppet-valves,  actuated  by  eccentrics, 
links,  and  levers  from  a  valve-shaft.  The  admission- valves 
are  controlled  by  the  governors.  Four  tests  were  made  on  this 
engine,  as  recorded  in  Table  XII. 


TABLE  XII. 

TRIPLE-EXPANSION   HORIZONTAL  MILL-ENGINE. 

CYLINDER    DIAMETERS    29.9,    44.5,    AND    TWO    OF    51.6    INCHES;    STROKE    78.7 

INCHES. 

Built  by  SULZER  of  Winterthur,  Zeitschrift  des    Vereins    Deutscher   Ingenieure, 

vol.  xl,  p.  534. 


I 

II 

III 

IV 

Duration,  minutes     .     .     . 
Revolutions  per  minute     . 
Steam-pressure,  pounds  per 
Vacuum   inches  of  mercury 

square  inch  . 

306 
56-23 
145-4 

27    24 

322 
56.28 
147.9 

27    2O 

272 
56.18 
148.4 
27   2O 

327 
56.18 
149.0 

27    IO 

Horse-power 

l872 

l8« 

i8co 

182? 

Steam  per  horse-power  per 
Mean  for  four  tests    .    . 
Coal  per  horse-power  per  he 
Mean  for  four  tests    .    . 
Steam  per  pound  of  coal  . 

hour,  pounds 
.    .    11.46  .    . 
>ur,  pounds     . 
.    .      1.30   .    . 

n-53 
J-37 
8.78 

11-49 
I.36 
8.49 

11.49 
1.29 
8.07 

n-33 

1.19 

962 

The  test  on  the  experimental  engine  at  the  Massachusetts 
Institute  of  Technology  is  quoted  here  because  its  efficiency 
and  economy  are  chosen  for  discussion  in  Chapter  VIII.  Taking 
its  performance  as  a  basis,  it  appears  on  page  148  that  with  150 
pounds  boiler- pressure  and  1.5  pounds  absolute  back-pressure 
such  an  engine  may  be  expected  to  give  a  horse-power  for  11.5 
pounds  of  steam,  from  which  it  appears  that  under  the  same 
conditions  its  performance  compares  favorably  with  the  Sulzer 
engine  or  even  the  Leavitt  engine. 


MARINE-ENGINE   TRIALS 


241 


TABLE   XIII. 

MARINE-ENGINE   TRIALS. 

By  Professor  ALEXANDER  B.  W.  KENNEDY,  Proc.  Inst.  Mech.  Engrs.,  1889-1892; 
summary  by  Professor  H.  T.  BEARE,  1894,  p.  33. 


I 
1 

Colchester. 

Ville  de 
Douvres. 

1 

1 

i-< 

Triple  or  compound   .            

r 

c 

C. 

T. 

T 

Diameter  high-pressure  cylinder,  inches      

27.4 

3O 

SO.  I 

20-4 

21.0 

Diameter  intermediate  cylinder,  inches  

44 

•24 

Diameter  low-pressure  cylinder,  inches 

CQ    "2 

r  7 

07    I 

7O   I 

^7 

Stroke,  inches      .                   ...            .            . 

•}•} 

?6 

72 

/w-  -1 
48 

•5Q 

Duration  of  trial,  hours                      .... 

14 

IO   O 

1  7 

16 

Number  of  expansions  .    . 

6  i 

6  i 

t?    7 

10  6 

10    O 

Revolutions  per  minute     . 

«  6 

86 

^6 

71.8 

61   i 

Steam-pressure    above  atmosphere,  pounds  per  square 
inch  

r6  8 

80    r 

icx  8 

14^  •  2 

r6r 

Pressure     in  condenser,  absolute,  pounds  per  square 
inch 

2     32 

2     £l 

472 

2    73 

O    7O 

Back-pressure,  absolute,  pounds  per  square  inch  .    .    . 
Horse-power 

3-8 
•771 

^  .  s,l 

3-4 

IO22 

6.0 

2Q77 

3-3 

1004 

1.8 

64  s: 

Steam  per  horse-power  per  hour,  pounds 

21     ^ 

T     7 

20    8 

I  e    O 

I  •?     A 

Thermal  units  per  horse-power  per  minute    
Coal  per  horse-power  per  hour,  pounds      .... 

380 

2  66 

398 
^    Q 

367 

2     3 

265 
2    OI 

250 
I     46 

Steam  evaporated  per  pound  of  coal   ........ 

7.06 

7  .  40 

8.07 

7.46 

O.I1? 

Weight  of  machinery  per  horse-power,  pounds      .    .    . 

603 

448 

272 

439 

701 

The  engines  of  the  S.  S.  lona  have  an  unusually  large  expansion 
and  give  a  correspondingly  good  economy.  The  engines  of  the 
Meteor  and  of  the  Brookline  give  the  usual  economy  to  be 
expected  from  medium-sized  marine  engines.  Table  XIII 
gives  details  of  tests  on  the  engines  of  the  first  two  ships 
mentioned,  together  with  tests  on  compound  marine  engines. 
Table  XIV  gives  tests  on  the  engine  of  the  Brookline.  It 
appears  probable  that  the  relatively  poor  economy  of  marine 
engines  compared  with  stationary  engines  is  due  to  the 
smaller  degree  of  expansion,  which  is  accepted  to  avoid  using 
large  and  heavy  engines. 


242 


ECONOMY   OF    STEAM-ENGINES 


TABLE  XIV. 

TESTS   ON   THE  ENGINE   OF  THE   S.  S.   BROOKLINE. 

CYLINDER   DIAMETERS    23,    35,    AND   57    INCHES;    STROKE   36   INCHES. 

By  F.  T.  MILLER  and  R.  G.  B.  SHERIDAN,  Thesis,  1895,  M.I.T. 


I 

II 

'ill 

IV 

V 

Duration,  hours        

2 

2 

I 

*A 

2i 

Revolutions  per  minute 

O4.    6 

a*  6 

cn  6 

Q-J 

Q-7 

Steam-pressure,  pounds  per  square   inch  above  at- 
mosphere              ...        ...        .... 

jrr 

I  CC 

154 

14.  tf 

148 

Vacuum,  inches  of  mercury    

21    6 

21    O 

22.  2 

21    7 

2O   O 

Horse-power     ...        

1242 

1221 

II36 

1137 

1148 

Steam  per  horse-power  per  hour,  pounds     .... 
Coal  per  horse-power  per  hour,  pounds   

17.2 

2  .  22 

16.9 
2.17 

15-5 
I  .99 

17.0 
2.l8 

16.3 

2  .OO 

B.T.U.  per  horse-power  per  minute     

292 

288 

263 

288 

277 

The  horizontal  mill-engine  which  heads  the  list  of  compound- 
engines  in  Table  X,  is  a  tandem  engine  for  which  particulars 
are  given  in  Table  XXVI  on  page  273.  Its  performance  with 
superheated  steam  is  the  best  among  the  engines  named,  and 
with  saturated  steam  is  a  trifle  superior  to  that  of  the  Louisville 
engine. 

TABLE  XV. 

COMPOUND   LEAVITT  PUMPING-ENGINE   AT  LOUISVILLE, 
KENTUCKY. 

CYLINDER   DIAMETERS    27.2    AND   54.!    INCHES;     STROKE    IO   FEET. 

By  F.  W.  DEAN,  Trans.  Am.  Soc.  Meek.  Engrs.,  vol.  xvi,  p.  169. 

Duration,  hours 144 

Revolutions  per  minute 18. 6 

Pressures,  pounds  per  square  inch: 

Barometric 14.6 

Boiler  above  atmosphere 140 

At  engine  above  atmosphere 137 

Back-pressure,  l.p.  cylinder 0.95 

Total  expansions      20 

Moisture  in  steam,  per  cent 0.55 

Horse-power 643.4 

Steam  per  horse-power  per  hour,  pounds 12.2 

B.T.U.  per  horse-power  per  minute 222 

Thermodynamic  efficiency,  per  cent 19 

Mechanical  efficiency,  per  cent 93 

This  engine  has  two  cylinders,  each  jacketed  with  steam  at 
boiler- pressure  on  barrels  and  heads,  and  steam  at  the  same 
pressure  is  used  in  a  tubular  reheater.  Each  cylinder  has  four 
gridiron  valves  actuated  by  as  many  cams  on  a  cam-shaft. 


AUTOMATIC    CUT-OFF    ENGINES 


243 


TABLE  XVII. 

ENGINES   OF  THE   U.  S.  REVENUE  STEAMERS   RUSH  AND 
GALL  A  TIN. 


Rush. 

U  all  a  tin. 

Diameters  of  cylinders,  inches  

24  and  38 

34.  I 

27 

3O 

rr 

24 

Revolutions  per  minute 

71 

r  i 

Steam-pressure  by  gauge  pounds  

00    I 

6c    A 

Vacuum  inches  of  mercury    

26    < 

2C     I 

Total  expansions          .        

6    2 

4   ^ 

Horse-power                  

266  c 

i6o.< 

Steam  per  horse-power  per  hour,  pounds    .... 

l8.4 

22 

The  details  of  the  tests  on  the  U.  S.  Revenue  Steamers  Rush 
and  Gallatin  are  given  in  Table  XVII,  as  made  about  1875  by 
a  board  of  naval  engineers  to  determine  the  advantages  of  com- 
pounding and  using  steam-jackets.  Three  other  engines  were 
tested  at  the  same  time,  but  they  were  of  older  types  and  are  less 
interesting. 

A  remarkably  complete  and  important  series  of  tests  was  made 
in  1884  by  M.  F.  Delafond.  These  tests  are  recorded  in  Tables 
XXX  and  XXXI,  from  which  there  are  quoted  in  Table  X  four 
results  with  and  without  condensation  and  with  and  without 
steam  in  the  jackets. 

TABLE  XVIII. 

AUTOMATIC  CUT-OFF  ENGINES. 

CYLINDER    DIAMETERS    1 8    INCHES;    STROKE    4    FEET. 

By  J.  W.  HILL. 
(First  Millers'  International  Exhibition,  Cincinnati,  1880.) 


Condensing. 

Non-condensing. 

R. 

H. 

W. 

R. 

H. 

W. 

10 

0.124 
75-4 
95-8 
29.7 
25-5 
4-5 
143-2 

20.6 

372 

10 
O.II9 

75-  8 
06.  i 
29.6 
25-7 
3-4 
145  -I 
19.4 
349 

10 

0.131 
74-5 
96.3 
29-4 
24.0 
4-7 
143-9 
19-5 
343 

0.160 

£3 

29.8 

iS-5 
121.7 
25-9 
433 

10 

0.136 
75-8 
96.3 
29.6 

14-9 
119.7 
23-9 
400 

10 
0.170 
76.1 
96.3 
29-5 

15-5  ' 
126.7 
24.9 

4i5 

Cut-off  

Revolutions  per  minute  

Boiler-pressure  above  atmos.Jbs.  per  sq.  in. 
Barometer,  inches  of  mercury    
Vacuum,  inches  of  mercury    
Back-pressure,  absolute,  ibs.  per  sq.  in.  . 
Horse-power     

Steam  per  horse-power  per  hour,  pounds 
B.T.U.  per  horse-power  per  hour  .  .  . 

244 


ECONOMY    OF    STEAM-ENGINES 


The  details  of  the  tests  on  the  Harris- Corliss  engine  at  Cin- 
cinnati, together  with  tests  on  two  similar  engines,  are  given  in 
Table  XVIII. 

TABLE  XIX. 

DUPLEX  DIRECT-ACTING   FIRE-PUMP  AT  THE  MASSACHUSETTS 
INSTITUTE   OF  TECHNOLOGY. 

TWO    STEAM-CYLINDERS    1 6   INCHES    DIAMETER,    12  INCHES   STROKE. 

Technology  Quarterly,  vol.  viii,  p.  19. 


Single 
strokes 

minute. 

Length 
of  stroke. 

West. 

Length 
of  stroke. 
East. 

Steam- 
pressure 
by  gauge. 

Horse- 
power. 
Steam- 
cylinders. 

Horse- 
power. 
Water- 
cylinders. 

Steam 
per  horse- 
power per 
hour. 

B.T.U. 
per  horse- 
power per 
minute. 

Duty.    (Foot, 
pounds  per 

1,  000,  COO 

B.T.U.) 

99 

II  .40 

10.  10 

58.5 

6.78 

I25 

2070 

13,920,000 

114 

II  .  70 

11.07 

55-6 

12.48 

101 

1674 

17,540,000 

119 

11.49 

11.07 

5i-4 

12.  l8 

109 

1809 

16,980,000 

!35 

1  1.  60 

II.  10 

53  •» 

18.24 

92 

153° 

19,850,000 

i5<> 

10.90 

10.26 

47-2 

2I.OO 

19.80 

98 

1619 

18,280,000 

i93 

10.09 

10.31 

45-6 

32-95 

78 

1291 

23,730,000 

i7S 

11.77 

11.79 

45  -6 

39-55 

66 

1083 

27,980,000 

1  80 

11.74 

11.66 

46.5 

41  .  2O 

67 

IIIO 

27,030,000 

TABLE  XX. 

TESTS    OF   AUXILIARY   STEAM   MACHINERY   OF   THE   U.  S.  S. 

MINNEAPOLIS. 

By  P.  A.  EngineetfW.  W.  WHITE,  U.  S.  N.,  Journal  Am.  Soc.  Naval 
Engrs.,  vol.  x. 


1 

J 
£  c 

rt   .£ 

il 

1 

j* 

I 

i, 

il 

*t?    £ 

!e 

£ 

"o 

0   g 

*© 

O 

f  S 

Engine  or  pump  tested. 

It 

g 

11 

is 

II 

M  "+3  aj 
•^"3  ^ 

uration 

dicated 
power. 

team  pe 
power  i 

1° 

5" 

3  ° 

* 

Q  " 

Q 

c 

w 

Centre  circulating-pump:        .    . 

Full  power   

IO 

36 

6 

6 

171.6 

3-7 

18.9 

55 

Reduced  power*     
Starboard  circulating-pump: 
Reduced  power     
Starboard  air-pump     .        ... 

10 
10 

16 

36 

36 
31.5 

6 
6 

21 

6 
6 

90 

82 
16.6 

2-50 

3-28 
2-58 

4.1 

2.0 

6.5 

76 

125 
183 

Centre  air-pump  t   

16 

21 

15-2 

3-2 

25.2 

78 

Water-service  pump     .        ... 
Fire-  and  feed-pump   .       ... 

7-5 

12 

4-5 
8-5 

10 
12 

7-5 
10.9 

40.9 
12.7 

2-59 

1.04 
0.78 

205 
319 

Do. 

12 

8-5 

12 

12  .O 

37.  3 

1-46 

6.4 

156 

Do  

12 

7-  5 

12 

10 

II.  0 

2-23 

8.8 

Do  

12 

7-  5 

12 

10.8 

2.6 

3—27 

1.6 

243 

Fire-and  bilge-pump 

14 

9 

12 

1  1  .  2 

27.  7 

2—2 

2.  5 

171 

Blower-engine  

5 

4 

4 

595 

1—24 

16.3 

77 

Dynamo-engine    .    .    . 

10.5 

'  '  ] 

5 

5 

425 

I-IO 

22.9 

65 

Do.         .    . 

5 

425 

O—26 

35-  2 

56 

Ice-machine  engine  .    .    . 

'5 

10 

IO 

73-  J 

5—12 

O  J 

6.0 

70 

*  One  cylinder  only  supplied  with  steam . 

t  Pump  loaded  with  three  times  the  power  developed  during  official  trial,  when  main  engine 
indicated  7219  H.P. 


METHODS   OF   IMPROVING    ECONOMY 


245 


The  two  tests  on  the  direct-acting  fire-pump  at  the 
Massachusetts  Institute  of  Technology  are  taken  from  Table 
XIX,  and  the  tests  on  the  feed-  and  fire-pump  on  the  Minneapolis 
are  given  in  Table  XX.  Both  sets  of  tests  show  the  extravagant 
consumption  of  steam  by  such  pumps  when  running  at  reduced 
powers.  The  latter  table  is  most  interesting  on  account  of  the 
light  that  it  throws  on  the  way  that  coal  is  consumed  by  a  war- 
vessel  when  cruising  at  slow  speeds  or  lying  in  harbor. 

Methods  of  Improving  Economy.  —  The  least  expensive  type 
of  engine  to  build  is  the  simple  non-condensing  engine  with  slide- 
valve  gear;  this  type  is  now  used  only  where  economy  is  of  little 
importance,  or  where  simplicity  is  thought  to  be  imperative. 
Starting  with  this  as  the  most  wasteful  type  of  engine,  improve- 
ments in  economy  may  be  sought  by  one  or  more  of  the  following 
devices : 

1.  Increasing  steam- pressure. 

2.  Condensing. 

3.  Increasing  size. 

4.  Expansion. 

5.  Compounding. 

6.  Steam-jackets. 

7.  Superheating. 

8.  The  binary  engine. 

An  investigation  of  the  conditions  under  which  these  various 
devices  can  be  used  to  advantage,  of  the  gain  to  be  expected, 
and  of  their  limitations,  is  one  of  the  most  interesting  and  impor- 
tant problems  for  the  engineer.  For  the  student  the  process  of 
such  an  investigation  is  even  of  more  importance  than  the 
conclusions,  because  by  it  he  may  learn  to  form  his  own  opinions 
and  may  take  account  of  other  tests  as  they  may  be  presented. 
The  order  chosen  is  to  some  extent  arbitrary,  and  cannot  be 
adhered  to  strictly,  as  the  tests  on  which  the  investigation  is 
based  were  made  for  various  purposes,  and  combine  the  several 
devices  in  various  manners. 

Of  these  devices  the  first  two  and  the  last  are  clearly  methods 
of  extending  the  temperature-range,  and  are  indicated  directly 


246  ECONOMY   OF   STEAM-ENGINES 

by  the  ideas  that  have  been  presented  in  the  general  discussion 
of  thermodynamics,  and  in  particular  by  the  adiabatic  theory  of 
the  steam-engine;  the  fourth  (expansion)  may  almost  be  included 
in  this  category  as  a  means  of  making  the  extension  of  temperature- 
range  effective.  It  has  been  seen  that  the  necessity  of  making 
the  cylinder  of  metal  which  is  a  good  conductor  and  has  an 
energetic  action  on  the  steam  in  the  cylinder,  interferes  with  our 
attempts  to  approach  the  efficiency  that  can  be  computed  for 
non-condensing  engines,  and  places  limitations  on  the  advantages 
to  be  gained  by  increasing  the  temperature-range.  The  other 
devices  enumerated  (increase  of  size,  compounding,  steam- 
jackets,  and  superheating)  are  various  methods  which  have 
been  applied  to  diminish  the  influence  of  the  cylinder  walls, 
and  allow  us  to  take  advantage  of  a  large  temperature-range.  It 
appears  at  first  sight  that  superheating  should  be  included  in 
the  first  category,  as  it  clearly  does  increase  the  temperature- 
range  between  the  steam-pipe  and  the  exhaust-pipe  of  the  engine, 
but  the  steam  in  the  cylinder  is  seldom  superheated  at  cut-off, 
and  it  is  better  to  consider  this  device  as  a  means  of  reducing 
cylinder  condensation. 

It  is  interesting  to  consider  that  condensation,  expansion,  and 
steam-jackets  were  used  by  Watt  for  his  earliest  engines,  and  that 
he  was  limited  in  pressure  by  the  condition  of  the  art  of  engineer- 
ing, so  that  there  was  no  occasion  for  compounding;  his  cylinders 
also  had  considerable  size,  though  the  powers  of  the  engines 
would  not  now  appear  to  be  large.  In  the  course  of  his  develop- 
ment of  the  true  steam-engine  from  the  atmospheric  engine, 
which  had  the  steam  condensed  in  the  cylinder  by  spraying  in 
water,  Watt's  attention  was  especially  directed  to  the  influence 
of  the  cylinder  walls ;  he  also  made  experiments  on  the  properties 
of  saturated  steam  within  the  range  of  available  pressures,  and 
had  such  an  appreciation  of  the  conditions  of  his  problem  that 
little  was  left  to  his  successors  except  to  learn  how  to  use  the 
higher  steam-pressures  which  the  developments  of  metallurgy 
and  machine-shop  practice  made  possible.  The  fact  that  our 
theory  of  the  steam-engine  was  developed  after  his  time,  and 


EFFECT    OF    RAISING    STEAM-PRESSURE  247 

that  the  theory  has  sometimes  been  misapplied,  has  given  an 
erroneous  opinion  that  the  steam-engine  has  been  developed 
without  or  in  spite  of  thermodynamics.  And  further,  his  use  of 
all  the  advantages  then  available  has  had  a  tendency  to  obscure 
their  importance,  and  makes  it  the  more  desirable  to  state  the 
several  methods  categorically  as  given  above. 

It  is  now  commonly  considered  that  the  steam-engine  has 
been  brought  to  full  development,  and  that  there  is  little  if  any 
substantial  improvement  to  be  expected;  in  fact,  this  condition 
was  reached  a  decade  or  two  ago,  when  the  triple  engine  using 
steam  at  150  to  175  pounds  by  the  gauge,  was  perfected.  The 
most  recent  change  is  the  use  of  superheated  steam  at  high 
pressures,  now  that  effective  and  durable  superheaters  have 
been  devised.  Experiment  and  experience  have  settled  fairly 
well  the  limitations  for  the  various  methods  of  improving  economy 
and  allow  of  a  fair  and  conservative  presentation  to  which  there 
will  probably  be  few  exceptions.  We  will,  therefore,  state  the 
general  conclusions  as  briefly  as  may  be,  and  give  the  tests  on 
which  they  may  be  based. 

In  order  to  bring  out  the  advantage  to  be  obtained  by  a  certain 
device,  such  as  compounding,  we  will  compare  only  the  best 
performance  of  the  simple  engine  with  the  best  performance  of 
the  compound  engine,  each  being  given  all  the  advantages  that 
it  can  use.  The  fact  that  marine  compound  engines  have  a 
worse  economy  than  stationary  simple-engines,  has  no  other 
meaning  for  our  present  purpose,  than  that  engines  on  ship- 
board are  subject  to  unfavorable  limitations. 

Effect  of  Raising  Steam-Pressure.  —  A  glance  at  the  table  on 
page  148  which  gives  the  efficiency  for  Carnot's  cycle,  will  show 
that  if  we  begin  with  a  low  steam-pressure,  there  is  a  large  advan- 
tage from  increasing  the  pressure  and  consequently  the  tem- 
perature-range, but  that  this  advantage  becomes  progressively 
less  marked.  This  conclusion  is  of  course  immediately  evident 
from  the  efficiency  for  Carnot  's  cycle,  which  may  be  written 

T  -  T 


248  ECONOMY    OF    STEAM-ENGINES 

If  tf  is  taken  to  be  100°  F.,  and  if  /  is -made  successively  200°, 
300°,  and  400°,  the  values  of  the  efficiency  are  0.15,  0.26,  and  0.35. 
But  the  influence  of  the  cylinder  quickly  puts  a  stop  to  this 
improvement  unless  we  resort  to  compounding,  as  will  be  seen  by 
studying  Delafond's  tests  in  Table  XXI,  page  250,  and  by 
Figs.  57  and  58  on  pages  252  and  253,  in  which  the  steam-con- 
sumption is  plotted  as  ordinates  on  the  fraction  of  the  stroke  at 
cut-off,  each  curve  being  lettered  with  the  steam-pressure  which 
was  maintained  while  a  series  of  tests  was  made.  Fig.  57  rep- 
resents tests  without  steam  in  the  jackets,  and  Fig.  58,  tests  with 
steam  in  the  jackets.  Those  curves  bearing  the  letter  C  were 
with  condensation,  and  those  bearing  the  letter  N  were  non- 
condensing.  Inspection  of  Fig.  57  shows  a  progressive  reduc- 
tion in  steam-consumption,  as  the  pressure  is  increased  from 
35  pounds  by  the  gauge  to  60  pounds  for  the  condensing  engine 
without  a  steam-jacket,  but  raising  the  pressure  from  60  pounds 
to  80  and  100  pounds  gives  a  marked  increase  in  steam-con- 
sumption. The  same  figure  indicates  that  100  pounds  is  probably 
the  limit  for  non-condensing,  unjacketed  engines.  The  curves 
on  Fig.  58  are  not  quite  so  conclusive;  but  we  may  from  both 
figures  give  the  following  as  the  best  pressures  to  be  used  with 
simple  engines  of  good  design  and  automatic  valve-gear: 

Desirable  Pressures  for  Simple  Engines. 

Condensing,  without  steam-jackets,  60  pounds  gauge. 

Condensing,  with  steam-jackets,  80  pounds  gauge. 

Non-condensing,  without  steam-jackets,      100  pounds  gauge. 

Non-condensing,  with  steam-jackets,  125  pounds  gauge. 

Delafond's  Tests.  —  In  1883  an  extensive  and  important 
investigation  was  made  by  Mons.  F.  Delafond  on  a  horizontal 
Corliss  engine  at  Creusot  to  determine  the  conditions  under 
•which  the  best  economy  can  be  obtained  for  such  an  engine. 
The  engine  had  a  steam-jacket  on  the  barrel,  but  was  not  jacketed 
on  the  ends.  Steam  was  supplied  to  the  jacket  by  a  branch 
from  the  main  steam-pipe,  and  the  condensed  water  was  drained 
through  a  steam-trap  into  a  can,  so  that  the  amount  of  steam 


DELAFOND'S   TESTS  249 

used  in  the  jacket  could  be  determined.  The  engine  was  tested 
with  and  without  steam  in  the  jacket,  both  condensing  and  non- 
condensing,  and  at  various  pressures  from  35  to  100  pounds 
above  the  pressure  of  the  atmosphere.  The  effective  power 
and  the  friction  of  the  engine  were  also  obtained  by  aid  of  a 
friction-brake  on  the  engine-shaft. 

The  piping  for  the  engine  was  so  arranged  that  steam  could  be 
drawn  either  from  a  general  main  steam-pipe  or  from  a  special 
boiler  used  only  during  the  test.  Before  making  a  test  the 
engine,  which  had  been  running  for  a  sufficient  time  to  come 
to  a  condition  of  thermal  equilibrium,  was  supplied  with  steam 
from  the  general  supply.  At  the  instant  for  beginning  the  test 
the  general  supply  was  shut  off  and  steam  was  taken  from  the 
special  boiler  during  and  until  the  end  of  the  test,  and  then  the 
pipe  from  that  boiler  was  closed.  The  advantage  of  this  method 
was  that  at  the  beginning  and  end  of  the  test  the  water  in  the 
boiler  was  quiescent  and  its  level  could  be  accurately  determined. 
At  the  end  of  a  test  the  water-level  was  brought  to  the  height 
noted  at  the  beginning.  The  water  required  for  feeding  the 
special  boiler  during  the  test  and  for  adjusting  the  water-level 
at  the  end  was  measured  in  a  calibrated  tank.  As  the  steam- 
pressure  in  the  general-supply  main  and  in  the  special  boiler 
was  the  same,  there  was  little  danger  of  leakage  through  the 
valves  for  controlling  the  steam-supply;  the  regularity  and  con- 
sistency of  results  shown  by  the  curves  of  Figs.  57  and  58  attest 
to  the  skill  and  accuracy  with  which  these  tests  were  made. 

Table  XXI  gives  the  results  of  tests  made  with  condensation, 
and  Table  XXII  gives  the  results  of  tests  without  condensation. 
All  the  tests  both  with  and  without  condensation,  but  during 
which  no  steam  was  used  in  the  jackets,  are  represented  by  the 
several  curves  of  Fig.  57,  while  Fig.  58  represents  tests  made 
with  steam  in  the  jackets.  The  curves  are  lettered  to  show  the 
mean  steam- pressure  for  the  series  represented  and  the  condition, 
whether  with  or  without  condensation.  Thus  on  Fig.  57  the 
lowest  curve  6oC  represents  tests  made  without  steam  in  the 
jackets  and  with  condensation,  while  the  highest  curve  on  Fig. 


25° 


ECONOMY   OF   STEAM-ENGINES 


58  represents  tests  with  steam  in  the  jackets  and  without  con- 
densation, at  50  pounds  boiler-pressure.  The  abscissae  for  the 
curves  are  the  per  cents  of  cut-off,  and  the  ordinates  are  the 
steam-consumptions  in  pounds  per  horse-power  per  hour.  The 

TABLE   XXI. 

HORIZONTAL   CORLISS   ENGINE   AT  CREUSOT. 
CYLINDER  DIAMETER  21.65  INCHES;  STROKE  43.31  INCHES;  JACKET  ON 

BARREL  ONLY;  CONDENSING. 
BY  F.  DELAFOND,  Annales  du  Mines,  1884. 


Number 
of  test. 

Duration, 
minutes. 

Revolu- 
tions per 
minute. 

Cut-off  in 
per  cent  of 
stroke. 

Steam- 
pressure, 
pounds  per 
sq.  in. 

Vacuum, 
inches  of 
mercury. 

Steam 
used  in 
jacket, 
per  cent. 

Indicated 
horse- 
power. 

Steam  per 
horse- 
power 
per  hour, 
pounds. 

i 

60 

60.0 

4 

96.3 

27.1 

109 

23.2 

2 

105 

58.6 

6 

98.8 

27.1 

128.5 

22.2 

3 

75 

59-4 

9 

IOO 

27.0 

161 

21.4 

4 

36 

57-7 

12.5 

99.1 

27.0 

186 

22.0 

5 

73 

58.8 

5-5 

104 

27-4 

"?' 

141 

I7.I 

6 

55 

61.5 

6.7 

102.4 

27.1 

? 

159-5 

l6.7 

7 

80 

59-9 

6.7 

103.8 

27.4 

2.9 

155 

16.5 

8 

39 

S8.i 

12.5 

105.2 

26.8 

3-2 

212 

17-6 

9 

1  20 

59-8 

7-5 

79-8 

27.1 

126 

21  .  2 

10 

100 

59-3 

8-3 

81.1 

27.4 

134 

21.  I 

ii 

90 

59-8 

10.5 

80.  i 

27.1 

ISO 

20.8 

12 

55-5 

58.0 

14 

85.5 

27.1 

175 

19.9 

13 

50 

59-1 

18 

84.8 

26.5 

194 

20.4 

14 

94 

59-6 

5 

85.1 

27.4 

3-o 

112 

17-7 

IS 

102 

59-6 

5-5 

83-3 

27.6 

3-1 

124 

17-3 

16 

40 

59-4 

ii.  5 

84.! 

27.1 

1.2 

176 

l6.9 

17 

40 

60 

14 

84-1 

27.0 

1-5 

193 

17-5 

18 

9i 

58-3 

5-9 

60.  5 

28.0 

85.3 

20.4 

19 

90 

59-5 

9 

55.8 

27.6 

us 

I9.I 

20 

75 

59-0 

15-5 

61.2 

27.8 

150 

18.1 

21 

75 

58.3 

22.7 

58.3 

27.6 

172 

18.4 

22 

3i 

59-2 

25 

61.2 

27.1 

1  86 

18.8 

23 

H5 

59-9 

6 

59-9 

27.8 

2.5 

91.7 

18.5 

24 

92 

59-6 

9 

59-9 

27.4 

2.5 

n7 

17.6 

25 

90 

58.8 

15-5 

60.9 

27.1 

1.8 

150 

17-3 

26 

7i 

59-1 

20 

61  .9 

26.8 

i-5 

i?5 

17.7 

27 

50 

59-o 

25 

62.3 

26.4 

1.6 

194 

18.6 

28 

70 

60.7 

6 

45-0 

28.0 

... 

75-6 

20.7 

29 

80 

58.8 

9-5 

48.9 

28.1 

94-3 

19.4 

3° 

in 

60.4 

15 

47-9 

27.6 

120 

18.8 

3i 

54 

58.8 

21 

47.8 

27.6 

140 

19.0 

32 

55 

59-4 

29 

47-6 

27.1 

165 

19.8 

33 

98 

60.3 

5 

45-8 

28.0 

2.6 

68.8 

19-3 

34 

63 

57-6 

10 

51-6 

27.6 

2.3 

95-5 

18.5 

35 

60 

59-7 

14-3 

49-1 

28.1 

1.4 

120 

18.2 

36 

74 

60.  i 

22 

48.6 

27.8 

1-4 

152 

18.9 

37 

50 

59-5 

29 

50-2 

26.8 

1.2 

179 

19.7 

38 

85 

60.3 

18.2 

33-1 

27.8 

... 

106 

20.5 

39 

68 

61.1 

43 

34-7 

26.5 

160 

22.7 

40 

42.5 

61.0 

56.7 

36.3 

26.0 

181 

25-3 

4i 

20 

60.0 

IOO 

31-7 

25.2 

182 

35-9 

42 

73 

60.7 

19 

32.0 

27.6 

1.6 

in 

19.8 

43 

80 

61  .  9 

42 

33-0 

26.5 

i.i 

162 

22.1 

44 

40 

6x.i 

58 

35-i 

26.0 

0.6 

180 

25.4 

45 

25 

60.4 

IOO 

34-7 

25.2 

0.2 

199 

33-0 

DELAFOND'S    TESTS 


251 


results  for  individual  tests  are  represented  by  dots,  through 
which  or  near  which  the  curves  are  drawn.  As  there  are  only 
a  few  tests  in  any  series,  a  fair  curve  representing  the  series  can 
be  drawn  through  all  the  points  in  most  cases.  The  exceptions 

TABLE  XXII. 

HORIZONTAL  CORLISS  ENGINE  AT  CREUSOT. 
CYLINDER  DIAMETER  21.65  INCHES;   STROKE  43.31  INCHES;   JACKET  ON  BARREL 

ONLY;  NON-CONDENSING. 
By  F.  DELAFOND,  Annales  des  Mines,  1884. 


Number  of 
test. 

Duration, 
minutes. 

Revolu- 
tions per 
minute. 

Cut-off  in 
per  cent  of 
stroke. 

Steam- 
prescure  , 
pounds  per 
Square  inch. 

Steam  used 
in  jacket, 
per  cent. 

Indicated 
horse- 
power. 

Steam  per 
horse-power 
per  hour, 
pounds. 

I 

78 

6l.7 

*3 

96.3 

J47-5 

28.4 

2 

55 

61.4 

17 

100.2 

.  .  . 

181.5 

26.8 

3 

25 

63.6 

2O 

102.  O 

217 

25.8 

4 

80 

60.8 

II 

98.1 

2-5 

143 

22.8 

5 

60 

62.0 

13 

103.8 

3.4 

177-5 

22.  I 

6 

36 

62.0 

16 

103.0 

3-i 

194 

22.4 

7 

3° 

62.7 

20 

I<>3-5 

2.O 

237 

21-5 

8 

66 

62.0 

!5-5 

73-7 

... 

121 

27.6 

9 

60 

60.9 

18 

77.0 

.  .  . 

136 

26.7 

10 

60 

6o.O 

24-5 

76.7 

I78 

24.6 

ii 

3° 

60.6 

32 

77-5 

209 

24.2 

12 

70 

61.1 

16.5 

77.0 

i-7 

137 

23-7 

13 

50 

61.6 

23-5 

75-8 

1.2 

180 

21.8 

14 

30 

60.5 

3° 

78.0 

i-3 

204 

22.0 

15 

7i 

61.4 

24-5 

50.8 

1  08 

27-3 

16 

70 

61.1 

37 

51.2 

147 

27.2 

17 

5° 

60.9 

58 

5°-5 

J73 

30.2 

18 

25 

60.6 

100 

34-9 

145 

46.8 

19 

70 

60.5 

23 

52.  6 

i-5 

108 

25-3 

20 

60 

60.5 

34 

51-8 

i.i 

i4i-5 

25.2 

21 

5° 

60.3 

58 

46.2 

0.7 

168.5 

28.7 

22 

30 

61.1 

100 

33-7 

°-3 

147-5 

46.3 

are  tests  made  with  condensation  for  boiler-pressure  of  80  and 
100  pounds  per  square  inch.  The  forms  of  the  curves  8oC 
and  looC,  Fig.  57,  were  made  to  correspond  in  a  general  way 
to  the  curves  5oC  and  6oC.  The  discrepancies  appear  large 
on  account  of  the  large  scale  for  ordinates,  but  they  are  not 
really  of  much  importance;  the  largest  deviation  of  a  point  from 
the  curve  looC  is  half  a  pound  out  of  about  22,  which  amounts 
to  little  more  than  two  per  cent.  On  Fig.  58  the  curve  8oC  is 
drawn  through  the  points,  but  though  its  form  does  not  differ 


252 


ECONOMY    OF    STEAM-ENGINES 


radically  from  the  curves  6oC  and  506*,  so  marked  a  minimum 
at  so  early  a  cut-off  is  at  least  doubtful.  Considering  that  the 
probable  error  of  determining  power  from  the  indicator  is  about 


\ 


18 


10 


20  30 

FIG.  57. 


50 


60 


two  per  cent,  it  would  not  be  difficult  to  draw  an  acceptable 
curve  in  place  of  8oC  which  should  correspond  to  the  forms  of 
6oC  and  506*. 

The  results  of  the  four  tests  made  with  steam  in  the  jacket 
and  with  condensation,  and  which  are  numbered  5,  6,  7,  and  8, 
in  Table  XXII,  are  represented  by  dots  inside  of  small  circles 


CONDENSATION 


253 


on  Fig.  58.     It  does  not  appear  worth  while  to  try  to  draw  a 
curve  to  represent  these  tests. 

Condensation.  —  The  complement  of  raising  the  steam-pressure 


30 


24 


22 


20 


18 


16 


\ 


10 


20 


30 
FIG.  58. 


40 


50 


is  the  use  of  a  condenser  with  a  good  vacuum.  The  advantage 
to  be  obtained  by  this  means  can  be  determined  from  Delafond's 
tests  by  aid  of  Figs.  57  and  58;  taking  the  best  conditions  as 
already  recorded  in  Table  X,  the  engine  without  a  jacket  and 
without  a  vacuum  used  24.2  pounds  of  steam  per  horse-power 
per  hour,  and  with  a  vacuum  it  used  18.1  pounds;  with  steam  in 
the  jackets  the  results  were  21.5  and  16.9.  A  direct  comparison 


254  ECONOMY   OF   STEAM-ENGINES 

of  either  pair  of  results  would  appear  to  give  a  saving  of  about 
25  per  cent,  which  would  be  manifestly  misleading.  The  results 
of  brake  tests  for  this  engine  on  page  292,  show  that  the  mechan- 
ical efficiency  when  running  non-condensing  was  0.90,  but  that 
it  was  only  0.82  when  running  condensing.  The  steam  per 
brake  horse-power  per  hour  can  be  obtained  by  dividing  the 
indicated  steam  by  the  mechanical  efficiency,  so  that  the  above 
pairs  of  results  became  for  the  engine  without  steam  in  the  jacket, 
non-condensing  26.9,  and  condensing  22.1,  and  for  the  engine 
with  steam  in  the  jacket,  23.9  and  20.6;  so  that  the  real  gain 
from  condensation  wras 

26.0  —  22.1  23.0  —  20.6 

— z— =  0.18  or  -i2-2 =  0.14. 

26.9  23.9 

The  gain  from  condensation  will  vary  with  the  type  of  engine 
and  the  conditions  of  service,  and  may  be  estimated  from  ten 
to  twenty  per  cent.  Clearly  the  gain  is  greater  with  a  good 
vacuum  than  with  a  poor  vacuum.  There  is,  however,  another 
feature  which  should  be  considered,  namely,  the  mean  effective 
pressure;  when  the  conditions  of  service  are  such  that  the  mean 
effective  pressure  is  large,  the  gain  from  condensation  and  the 
advantage  of  maintaining  a  good  vacuum  are  not  so  great  as 
when  the  mean  effective  pressure  is  small.  This  feature  can 
be  best  illustrated  with  examples  of  triple-expansion  engines, 
which  are  able  to  work  advantageously  with  a  large  total  expan- 
sion, and  for  them  we  may  deal  with  the  reduced  mean  effective 
pressure,  meaning  by  that  expression  the  result  obtained  by  the 
following  process:  the  mean  effective  pressure  for  the  high- 
pressure  cylinder  is  to  be  multiplied  by  the  area  of  that  piston 
and  divided  by  the  area  of  the  low-pressure  piston;  the  mean 
effective  pressure  for  the  intermediate  cylinder  is  to  be  treated 
in  a  similar  way;  the  two  results  are  then  to  be  added  to  the 
mean  effective  pressure  for  the  low-pressure  cylinder;  clearly 
this  sum,  which  is  called  the  reduced  mean  effective  pressure, 
if  it  were  applied  to  the  low-pressure  piston  would  develop  the 
actual  power  of  the  engine.  Now  the  reduced  mean  effective 


INCREASE    OF    SIZE  255 

pressure  for  a  pumping-engine  or  mill-engine  may  be  as  low  as 
1 8  pounds  per  square  inch,  and  a  difference  of  one  inch  of 
vacuum  (or  half  a  pound  of  back- pressure)  will  be  equivalent 
to  nearly  three  per  cent  in  the  power;  on  the  other  hand,  a  naval 
engine  is  likely  to  have  a  reduced  mean  effective  pressure  of 
forty  pounds  per  square  inch,  and  compared  with  it  a  difference 
of  one  inch  of  vacuum  is  equivalent  to  a  little  more  than  one  per 
cent.  In  any  case  the  gain  in  economy  due  to  a  small  improve- 
ment in  vacuum  is  approximately  equal  to  the  reduction  in  the 
absolute  pressure  in  the  condenser,  divided  by  the  reduced 
mean  effective  pressure. 

A  very  important  matter  is  brought  out  in  this  discussion  of 
the  gain  from  condensation,  namely,  that  the  real  gain  is  deter- 
mined by  comparing  the  engine  consumption  for  the  net  or 
brake  horse-powers.  The  only  reason  for  using  the  indicated 
power  (as  is  most  commonly  done)  is  that  the  brake-power  is 
often  difficult  to  determine  and  sometimes  impossible.  As 
was  pointed  out  on  page  144,  a  true  basis  of  comparison  is  the 
heat-consumption  of  the  engines  compared  in  B.T.U.  per  horse- 
power per  hour.  But  that  quantity  was  not  determined  for  the 
tests  by  Delafond,  and  since  the  comparisons  are  for  two  pairs 
of  tests,  one  pair  with  and  the  other  without  jackets  there  is  no 
objection  to  it  in  the  cases  discussed. 

Increase  of  Size.  —  Since  the  failure  to  attain  the  economy 
computed  for  the  non-conducting  engine  is  due  mainly  to  the 
action  of  the  cylinder  walls,  and  since  the  volume  of  the  cylinder 
are  proportional  to  the  cube  of  a  linear  dimension,  while  the  sur- 
face is  only  proportional  to  the  square,  a  great  advantage  might 
be  expected  by  simply  increasing  the  size  of  the  engine.  Such 
an  advantage  is  indicated  by  the  comparison  of  the  small  Harris- 
Corliss  engine  at  the  Massachusetts  Institute  of  Technology  with 
the  Corliss  engine  at  Creusot,  the  steam-consumption  without 
condensation  or  steam-jackets  being  33.5  pounds  and  24.2  pounds 
per  horse-power  per  hour,  and  the  gain  from  increase  of 
size  being 

ais^ta  _  o-2g_ 

33-5 


256  ECONOMY   OF   STEAM-ENGINES 

In  this  case  the  larger  engine  has  about  twelve  times  the  cylinder 
capacity  of  the  smaller  one.  This  feature  appears  to  depend  on 
the  absolute  size  of  the  engine,  because,  as  will  appear  later,  there 
is  little  if  any  advantage  in  speed  of  rotation  within  the  usual 
limits  of  practice. 

But  the  advantage  from  increase  of  size  soon  reaches  a  limit, 
as  will  be  apparent  from  the  consideration  that  the  best  results 
in  Table  X  are  for  engines  of  moderate  power,  judged  by  modern 
standards.  These  engines  have  the  advantages  of  compounding, 
and  of  the  use  of  steam-jackets  or  superheated  steam;  the  advan- 
tages from  jacketing  or  superheating  decrease  with  the  size, 
and  such  devices  are  possibly  of  little  advantage  to  massive 
engines. 

Expansion.  —  There  are  two  limits  to  the  amount  of  expansion 
that  can  be  advantageously  used  for  a  given  engine:  one  limit 
is  imposed  by  the.  action  of  the  cylinder  walls,  and  the  other  is 
imposed  by  the  friction  of  the  engine.  Simple  engines  have  the 
most  advantageous  point  of  cut-off  determined  by  the  first  limit, 
which  can  be  clearly  determined  by  aid  of  Delafond's  experi- 
ments; compound  and  triple- expansion  engines  so  divide  up 
the  temperature-range  that  any  desirable  expansion  can  be 
employed.  The  terminal  pressure  at  the  end  of  expansion  for 
a  stationary,  triple,  or  compound  engine  may  be  made  as  low  as 
five  pounds  absolute;  and  as  the  back- pressure  is  likely  to  be 
a  pound  or  a  pound  and  a  half,  so  that  the  terminal  effective 
pressure  is  three  and  a  half  or  four  pounds,  and  as  it  takes  about 
two  pounds  per  square  inch  to  drive  the  piston  and  connected 
parts,  there  is  evidently  little  to  be  gained  in  economy  by  further 
expansion. 

As  for  simple  engines,  an  inspection  of  Figs.  57  and  58  on  pages 
252  and  253  shows  that  the  best  point  of  cut-off  for  non-conden- 
sing engines  is  one-third  stroke,  and  for  condensing  engines  about 
one  sixth-stroke;  if  the  engine  has  a  steam-jacket,  the  cut-off 
may  be  a  little  earlier  than  one-sixth  stroke,  but  there  probably 
is  little  advantage  from  such  an  increase  of  expansion  if  we  deal 
with  the  net  or  brake  horse-power. 


COMPOUNDING  257 

The  total  expansion  for  a  compound  or  triple  engine  can  be 
obtained  in  two  ways:  we  may  use  a  large  ratio  of  the  large 
cylinder  to  the  small  cylinder,  or  we  may  use  a  short  cut-off  for 
the  high-pressure  cylinder.  The  two  methods  may  be  illustrated 
by  the  two  Leavitt  engines  mentioned  in  Table  X;  the  ratio  of 
the  large  to  the  small  cylinder  of  the  compound  engine  at 
Louisville,  is  a  trifle  less  than  four,  and  the  cut-off  for  the  high- 
pressure  cylinder  is  a  little  less  than  one-fifth  stroke;  on  the 
other  hand,  the  triple  engine  at  Chestnut  Hill  has  a  little  more 
than  eight  for  the  extreme  ratio  of  the  cylinders,  and  has  the 
cut-off  for  the  high-pressure  cylinder  at  a  little  more  than  four- 
fifths.  So  large  an  extreme  ratio  as  eight  would  not  be  con- 
venient for  a  compound  engine,  but  ratios  of  five  or  six  have 
been  used,  though  not  with  the  best  results. 

Marine  engines  usually  have  comparatively  little  total  expan- 
sion both  for  compound  and  for  triple  engines,  and  consequently 
are  unable  to  work  with  an  economy  equal  to  that  for  stationary 
engines ;  the  type  of  valve-gear  which  the  designers  feel  constrained 
to  use  is  also  little  adapted  to  give  the  best  results.  There  is 
some  question  whether  there  is  not  room  for  improvement  in 
both  these  directions. 

Compounding.  —  The  most  efficacious  method  which  has 
been  devised  to  increase  the  amount  of  expansion  of  steam  in 
an  engine,  and  at  the  same  time  to  avoid  excessive  cylinder- 
condensation,  is  compounding;  that  is,  passing  the  steam  in 
succession  through  two  or  more  cylinders  of  increasing  size. 
An  engine  with  two  cylinders,  a  small  or  high-pressure  cylinder 
and  a  large  or  low-pressure  cylinder,  is  called  a  compound 
engine.  An  engine  with  three  cylinders,  a  high-pressure  cylinder, 
an  intermediate  cylinder,  and  a  low-pressure  cylinder,  is  called 
a  triple-expansion  engine.  A  quadruple  engine  has  a  high- 
pressure  cylinder,  a  first  and  a  second  intermediate  cylinder, 
and  a  low-pressure  cylinder.  Any  cylinder  of  a  compound  or 
multiple-expansion  engine  may  be  duplicated,  that  is,  may  be 
replaced  by  two  cylinders  which  are  usually  of  the  same  size. 
Thus,  at  one  time  a  compound  engine  with  one  high-pressure 


258  ECONOMY    OF    STEAM-ENGINES 

and  two  low-pressure  cylinders  was  much  used  for  large  steam- 
ships. Many  triple  engines  have  two  low-pressure  cylinders, 
which  with  the  high-pressure  and  the  intermediate  cylinders 
make  four  in  all.  Again,  some  triple  engines  have  two  high- 
pressure  cylinders  and  two  low-pressure  cylinders  and  one 
intermediate  cylinder,  making  five  in  all. 

Two  questions  arise:  (i)  Under  what  conditions  should  the 
several  types  of  engines  be  used?  and  (2)  What  gain  can  be  ex- 
pected by  using  compound  or  triple  expansion  ? 

Neither  question  can  be  answered  explicitly. 

From  tests  already  discussed  and  for  which  the  main  results 
are  given  in  Table  X,  it  appears  that  with  saturated  steam,  the 
best  results  were  attained  with  the  following  pressures :  for  triple 
engines  about  175  pounds  by  the  gauge,  for  compound  engines 
145  pounds,  and  for  simple  engines  with  about  80  pounds,  all 
for  engines  with  condensation.  Nearly  as  good  results  were 
obtained  for  a  compound  engine  with  135  pounds  pressure, 
and  on  the  other  hand  the  simple  engine  could  use  106  pounds 
with  equal  advantage.  The  information  concerning  the  simple 
engine  is  sufficient  to  serve  as  a  reliable  guide,  but  there  is  at 
least  room  for  discretion  concerning  the  best  pressures  for  com- 
pound and  triple  engines.  There  will  probably  be  little  chance 
of  serious  disappointment  if  the  following  table  is  used  as  a  guide 
in  designing  engines,  all  being  with  condensation  and  with 
steam-jackets. 

Best  Gauge-Pressures  for  Steam- Engines. 

Simple 80 

Compound 140 

Triple 175 

If  for  any  reason  it  is  desired  to  use  a  higher  or  lower  pressure 
in  any  case,  a  variation  of  20  pounds  either  way  may  be  assumed 
without  much  loss  of  efficiency;  this,  however,  cannot  be  stated 
quantitatively  at  the  present  time. 

For  non-condensing  simple  engines  the  pressure  should 
preferably  be  100  pounds  without  a  steam-jacket,  and  125 


COMPOUNDING 


259 


pounds  with  a  steam-jacket;  with  an  allowable  variation  of  twenty 
pounds.  For  a  non-condensing  compound  engine  we  may  take 
as  the  preferred  pressure  about  175  pounds,  but  our  tests  do  not 
include  this  case,  and  the  figure  is  open  to  question.  There  is 
little,  if  any,  occasion  for  using  triple-expansion  non-condensing 
engines. 

About  ten  years  ago  an  attempt  was  made  to  introduce  quad- 
ruple-expansion engines,  using  steam  at  about  250  pounds  for 
marine  purposes  in  conjunction  with  water-tube  boilers,  which 
can  readily  be  built  for  high-pressures;  but  more  recent  practice 
has  been  to  adhere  to  triple  engines  even  where  the  designer 
has  chosen  a  high-pressure  for  sake  of  developing  a  large  power 
per  ton  of  machinery,  or  for  any  other  purpose. 

For  convenience  in  trying  to  determine  the  gain  from  com- 
pounding, the  following  supplementary  table  has  been  drawn  off. 


Data  and  Results. 

Simple 
Corliss  at 
Creusot. 

Compound 
Mill-Engine- 

Triple 
Leavitt  at 
Chestnut 
Hill. 

Revolutions  per  minute 

60 

fQ      ^ 

Steam-pressure  above  atmosphere,  pounds  .    . 

84 

I48 

176 

Total  expansion 

9 

2O 

21 

SteRm  per  horse-power  per  hour,  pounds  .    .    . 

16.9 

ii.  8 

ii.  a 

B.T.U.  per  horse-power  per  minute  

220 

204 

Gain  from  compounding, 

16.9  —  ii. 8 
16.9 


=  0.30. 


Gain  from  using  triple  engine  in  place  of  simple  engine, 
16.0  —  ii.  2 


Gain  from  using  triple  engine  in  place  of  compound  engine 
n.8  —  ii.  2 


n.8 


'0.05, 


260 


ECONOMY   OF   STEAM-ENGINES 


Compound  and  triple  engines  have  been  found  well  adapted 
to  marine  work,  where  for  various  reasons  a  short  cut-off  cannot 
well  be  used.  Taking  the  engines  of  the  three  ships  mentioned 
in  the  following  supplementary  table  to  represent  good  practice, 
we  can  determine  the  gain  from  compounding. 


Data  and  Results. 

Simple 
Galatin. 

Compound 
Rush. 

Triple 
Meteor. 

Revolutions  per  minute       ......... 
Steam  pressure  by  gauge             .               . 

5T 
6<c 

71 
60 

72 
14? 

Total  expansion                         .        ....        . 

4e 

6    2 

Lf*3 

TO.  6 

Steam  per  horse-power  per  hour,  pounds  . 

22 

18.4 

15 

Gain  from  compounding, 


22  —  18.4 


=  0.16. 


22 


Gain  from  using  triple  engine  instead  of  simple  engine, 
22  —  15 


22 


0.32, 


Gain  from  using  triple  engine  instead  of  compound  engine, 


=  0.18. 


Two  things  are  to  be  noted:  first,  that  the  total  number  of 
expansions  is  very  moderate  even  for  the  triple  engine;  and, 
second,  that  the  steam-consumption  is  correspondingly  large 
as  compared  with  that  for  stationary  engines. 

A  notable  exception  in  marine  practice  is  the  engine  of  the 
lona,  which  was  relatively  much  larger  than  can  commonly  be 
placed  in  a  steamer;  it  had  the  advantage  of  165  pounds  steam- 
pressure  and  19  total  expansions,  and  had  a  steam-consumption 
of  only  13  pounds  per  horse-  power  per  hour. 


EXPERIMENTAL   ENGINE  261 

Properly  the  comparison  for  finding  the  gain  from  compound- 
ing should  be  based  on  thermal  units  per  horse-power  per  minute, 
but  the  data  for  such  a  comparison  are  not  given  for  all  the 
engines,  and  as  all  the  engines  have  steam-jackets,  the  comparison 
of  steam-consumptions  is  not  much  in  error. 

Steam-jackets.  —  As  has  already  been  pointed  out  in  the 
discussion  of  the  influence  of  the  cylinder  walls,  the  beneficial 
action  of  a  steam-jacket  is  to  dry  out  the  cylinder  during  exhaust, 
without  unduly  reducing  the  temperature  of  the  cylinder  walls, 
and  thus  check  the  condensation  during  admission.  The  steam- 
jacket  does  indeed  supply  some  heat  during  expansion,  but 
that  effect  is  of  secondary  importance,  and  the  heat  is  applied 
with  a  thermodynamic  disadvantage.  The  principal  effect  is 
thus  to  supply  heat  which  is  thrown  out  in  the  exhaust,  which  is 
all  lost  in  case  of  a  simple  engine;  in  case  of  a  compound  engine 
the  heat  supplied  by  a  jacket  during  exhaust  from  the  high- 
pressure  cylinder  is  intercepted  by  the  low-pressure  cylinder, 
and  is  not  entirely  lost.  It  would  clearly  be  much  more  advan- 
tageous to  make  the  cylinders  of  non-conducting  material,  if 
that  were  possible.  A  clear  grasp  of  the  true  action  of  the 
steam-jacket  has  a  natural  tendency  to  prejudice  the  mind 
against  that  device,  and  this  prejudice  has  in  many  cases  been 
strengthened  by  the  confusion  that  has  come  from  indiscriminate 
comparison  of  many  tests  made  to  determine  the  advantage 
from  the  use  of  steam-jackets. 

There  are  two  series  of  tests  that  appear  to  dispose  of  this 
question,  —  those  by  Delafond  on  the  Corliss  engine  at  Creusot, 
and  those  made  at  the  Massachusetts  Institute  of  Technology 
on  a  triple-expansion  experimental  engine;  the  former  has  already 
been  given,  and  the  latter  will  now  be  detailed;  afterward  the 
gain  from  the  use  of  the  jacket  will  be  discussed. 

Experimental  Engine  at  the  Massachusetts  Institute  of 
Technology.  —  This  engine,  which  was  added  to  the  equipment 
of  the  laboratory  of  steam-engineering  of  the  Institute  in  1890, 
is  specially  arranged  for  giving  instruction  in  making  engine-tests. 
It  has  three  horizontal  cylinders  and  two  intermediate  receivers, 


262  ECONOMY   OF    STEAM-ENGINES 

the  piping  being  so  arranged  that  any  cylinder  may  be  used 


3GO 


310 


300 


280 


260 


240 


200 


\ 

tr 

\ 

\ 

X 

s 

N 

-7C 

ompou 

nd, 

X 

/ 

w 

ithout 

jacket 

^ 

s\ 

\ 

\ 

•s 

\ 

\, 

<, 

^ 

V 

X 

<^ 

s 

^ 

^Trip 
witt 

le, 
out  jac 

;kets 

\ 

/  ^s 

^ 

•*-*2_^ 

Tr^ 
^  on 

plej'ac 
heads 

kets 

• 

\ 

\ 

\ 

\v 

Vvf 

.S 

Trii 
on  c 
^  and 

lejacl 
ylinde 
receiv 

ets 
jr 

x 

• 
• 

^^ 

r^**^ 

^ 

Triple,  ja 
*\on  cylindei 

jkets 
s  only 

10 


20         30 
FIG.  59 


singly  or  may  be  combined  with  one  or  both  of  the  other  cylinders 
to  form  a  compound  or  a  triple  engine.     Each  cylinder  has 


OF 

UNIVER 

CF  « 


PERIMENTAL   ENGINE  263 


steam-jackets  on  the  barrel  and  the  heads,  and  steam  may  be 
supplied  to  any  or  all  of  these  jackets  at  will.  The  steam  con- 
densed in  the  jackets  of  any  one  of  the  cylinders  is  collected  under 
pressure  in  a  closed  receptacle  and  measured.  Originally  the 
receivers  were  also  provided  with  steam-jackets;  now  they  are 
provided  with  tubular  reheaters  so  divided  that  one-third,  two- 
thirds,  or  all  the  surface  of  the  reheaters  can  be  used..  The 
steam  condensed  in  the  reheaters  is  also  collected  and  measured 
in  a  closed  receptacle. 

The  valve-gear  is  of  the  Corliss  type  with  vacuum  dash-pots 
which  give  a  very  sharp  cut-off.  The  high-  pressure  and  inter- 
mediate cylinders  have  only  one  eccentric  and  wrist-plate,  and 
consequently  cannot  have  a  longer  cut-off  than  half  stroke  under 
the  control  of  the  drop  cut-off  mechanism.  The  low-pressure 
cylinder  has  two  eccentrics  and  two  wrist-plates,  and  the  admission 
valves  can  be  set  to  give  a  cut-off  beyond  half  stroke.  The 
governor  is  arranged  to  control  the  valves  for  any  or  all  of  the 
cylinders.  Each  cylinder  has  also  a  hand-gear  for  controlling 
its  valves.  For  experimental  purposes  the  governor  is  set  to 
control  only  the  high-pressure  valve-gear,  when  the  engine  is 
running  compound  or  triple-expansion.  The  hand-gear  is 
used  for  adjusting  the  cut-off  for  the  other  cylinder  or  cylinders; 
usually  the  cut-off  for  such  cylinder  or  cylinders  is  set  to  give  a 
very  small  drop  between  the  cylinders.  This  arrangement 
throws  a  very  small  duty  on  the  governor,  so  that  by  the  aid  of 
a  large  and  heavy  fly-wheel  the  engine  can  be  made  to  give 
nearly  identical  indicator-diagrams  for  an  entire  test  during 
which  the  load  and  the  steam-pressure  are  kept  constant. 

The  main  dimensions  of  the  engine  are  as  follows: 

Diameter  of  the  high-pressure  cylinder   .......  9       inches. 

intermediate          "          .....  ..  16 

'  '       low-pressure          "         .......  24          '  ' 

"  "       piston-rods     ......  .  ..........       2^      " 

Stroke  ......................................  30          " 


264  ECONOMY    OF   STEAM-ENGINES 

Clearance  in  per  cent  of  the  piston  displacements : 

High- pressure  cylinder,  head  end,     8.83;     crank  end,     9.76 
Intermediate  "  "        "      10.4  "        "      10.9 

Low-pressure          "  "       "11.25  "        "       8.84 

Results  of  tests  on  the  engine  with  the  cylinders  arranged  in 
order  to  form  a  triple-expansion  engine  are  given  in  Table 
XXIII,  and  are  represented  by  the  diagram  Fig.  60  with  the 
cut-off  of  the  high-pressure  cylinder  for  abscissae  and  with  the 
consumptions  of  thermal  units  per  horse-power  per  minute  as 
ordinates. 

The  most  important  investigation  which  has  been  made  on 
this  engine  is  of  the  advantage  to  be  obtained  from  the  use  of 
steam  in  the  jackets.  Four  series  of  tests  were  made  for  this 
purpose:  (i)  with  steam  in  all  the  jackets  of  the  cylinders  and 
receivers,  (2)  with  steam  in  the  jackets  of  the  cylinders,  both 
heads  and  barrels,  (3)  with  steam  in  the  jackets  on  the  heads  of 
the  cylinders  only,  and  (4)  without  steam  in  any  of  the  jackets. 

The  most  economical  method  of  running  the  engine  was  with 
steam  in  all  the  jackets  on  the  cylinders,  but  without  steam  in 
the  receiver-jackets,  as  shown  by  the  lowest  curve  on  Fig.  59. 
There  is  a  small  but  distinct  disadvantage  from  using  steam  in 
the  receiver-jackets  also.  This  fact  could  not  be  surely  deter- 
mined from  any  pair  of  tests,  for  the  difference  is  not  more  than 
two  per  cent,  and  is  therefore  not  more  than  the  probable  error 
for  such  a  pair  of  tests,  but  a  comparison  of  the  two  curves  on 
Fig.  59,  representing  tests  under  the  two  conditions,  gives  con- 
clusive evidence  with  regard  to  this  point.  It  may  not  be  im- 
proper in  this  connection  to  call  attention  to  the  three  points 
below  the  lowest  curve  and  not  connected  with  it ;  they  represent 
tests  which  were  made  after  the  nine  tests  represented  by  points 
joined  to  the  curve,  and  when  some  additional  non-conducting 
covering  had  been  applied  to  the  piping  and  valves  of  the  engine. 
Here  the  slight  gain  from  reduced  radiation  is  made  manifest, 
though  it  is  too  small  to  be  taken  into  account  in  making  com- 
parisons of  the  different  conditions  of  running  the  engine. 


EXPERIMENTAL   ENGINE 


265 


TABLE  XXIII. 

TRIPLE-EXPANSION   EXPERIMENTAL    ENGINE   AT  THE   MASSA- 
CHUSETTS  INSTITUTE   OF  TECHNOLOGY. 

Trans.  Am.  Soc.  Mech.  Engs.,  1892-1894;   Technology  Quarterly,  1896. 


Steam  used  in  jackets, 

per  cent. 

.    . 

u 

-a 

i 

II 

3 

J3    »H 

a 

$Z 

•8 

In 

.jj 

| 

8- 

Is 

H 

o  B 

3s 

*T1    S 

OJ 

u 

1 

oi 

•  % 

& 

3 

8S 

1& 

g 

to 

S 

u 

g     . 

v  «l 

Wo 

I 

Revolutions 

iPer  cent  of 
pressure 

Boiler-press 

Vacuum  in 
inches  of 

Barometer, 
merci 

ir 

First  receive 

Intermediat 
sure  cylin 

! 

I1 

S 

Steam  per  h 
per  hou 

3 

PQ 

PQ 

i 

89-93 

36.1 

146.2 

24.1 

29.8 

3-2 

8.6 

6.3 

140.8 

n  8 

240 

233 

2     a 

90.60 

35-0 

147.0 

24.7 

30-3 

2-5 

8.8 

5-4 

138.0 

J3-9 

241 

237 

91-93 

27-3 

146.9 

24-5 

29.9 

2-5 

8-5 

7.2 

125.4 

13-7 

237 

231 

4    -55  TJ 

91-55 

27.0 

146.7 

25-4 

30.1 

3-2 

9.8 

8.1 

123.9 

13-7 

239 

230 

92.37 

25-0 

146.6 

24-5 

30.7 

3-4 

10.^5 

10.  I 

114.7 

14-3 

247 

240 

6       rt">, 

84-87 

21.9 

145-2 

24-3 

30.1 

3-5 

1  1  •  3 

8.7 

105-3 

14-5 

250 

241 

7    *""*  ° 

93-  1  5 

17.4 

146.0 

26.0 

3O.  2 

3  5 

10.7 

ii.  6 

103.  5 

255 

255 

8 

86.70 

12.0 

147.0 

27-4 

30-5 

6.1 

15-2 

12.2 

78.3 

i5-i 

261 

273 

9 

87.55 

8.3 

146.7 

26.0 

30.1 

6.5 



15-3 

13-0 

67.4 

16.0 

274 

274 

10 

84.23 

13-5 

145-2 

26.1 

30.0 

5-3 

11.3 

12.  I 

77-8 

14-7 

253 

255 

ii  Ditto. 

82.50 

20.5 

144-5 

26.2 

29-9 

4-5 

9.1 

9-9 

101.9 

13-5 

235 

237 

12 

82.  13 

23-6 

145-3 

20.4 

30.1 

3-1 



8-5 

9.8 

104.2 

13-3 

232 

235 

13    CT3     . 

91.20 

36.1 

143-7 

24.7 

30.2 

2.6 

4-7 

6.4 

f-4 

5-9 

154-2 

14.4 

249 

244 

I4    §  |  tn 

91.40 

32.8 

143-6 

25-0 

30.2 

2-9 

6.4 

7-  1 

4-  3 

6.4 

I45-I 

14.  i 

244 

240 

16  III 

91.82 
91.83 

29-3 

27-5 

143-2 
147.1 

25-2 
24-7 

30.5 
30,3 

3.o 
1.4 

5-6 
4-7 

7.6 
8.9 

4-9 

6.1 

7-3 

128  '.  8 

14-3 
14.1 

246 
242 

243 
237 

92.17 

25-9 

145-5 

25-5 

30-4 

3-2 

4-5 

8.2 

4-7 

5-7 

125.8 

14.1 

243 

241 

ig  ^UM 

92.57 

21.9 

143-7 

26.4 

30.6 

3-4 

6.8 

7-i 

7-7 

120.2 

14.6 

256 

258 

19 

84.95 

9-i 

145-8 

25-6 

30.0 

2-9 

7-7 

8.7 

55-9 

16.6 

290 

285 

20       j.. 

84-03 

13-9 

144-5 

26.4 

29-9 

2.1 

7-2 

8.6 

60.4 

15-5 

273 

277 

21       0     . 

83-35 

15.6 

144.9 

25-6 

29.8 

2.2 

6.8 

8.0 

72.8 

I5-  5 

273 

269 

22       §•§ 

82.40 

20.7 

145-3 

26.7 

30.3 

1.4 

6.6 

8.0 

84.2 

i5-i 

269 

23     ^J 

81.40 

27-3 

144.2 

24-7 

29-7 

7-7 

5-6 

97-4 

15-2 

267 

261 

24    rt45 

81.05 

29-7 

J43-4 

25-4 

29-9 

1.4 

5-3 

6.8 

101.5 

15.0 

26s 

263 

25  ""» 

80.28 

34-9 

I43-I 

25.5 

30.2 

1.2 

5-0 

6.4 

109.4 

15.0 

265 

262 

26 

80.32 

35-6 

144.0 

25-0 

29-9 

I.  I 

4-6 

7-4 

114.1 

15-2 

267 

264 

27 

85  60 

8.4 

152  8 

26  i 

29  7 

53   2 

3I8 

318 

28 

85.62 

8.1 

153-3 

26.1 

55-7 

16.9 

308 

29 

85.60 

10.6 

152-1 

26.1 

29-9 

60.6 

16.2 

206 

297 

30 

84.22 

15.8 

152.8 

25.0 

29.8 

74-  9 

15  4 

287 

086 

31 

83-03 

21.3 

152.0 

26.3 

85.8 

276 

277 

32          „; 

82.92 

21.2 

152.4 

26.09 

30.  15 

86.9 

15.4 

281 

33        *> 

82.55 

21  .0 

153.0 

26.02 

30.0 

87.8 

15    2 

284 

284 

34  -a 

83.32 

24.1 

152.0 

25.70 

91  .  i 

15.  5 

280 

35      •- 

82.67 

29-5 

151-9 

25.6 

30.0 

99-9 

15-5 

283 

280 

36      £ 

81.78 

29.  I 

152.0 

25.7 

100.  5 

15.  2 

275 

273 

37      ^ 

82  92 

•>«  7 

26  o 

38 

81.52 

30.7 

I5I.5 

26.1 

29-9 

106.0 

15-2 

278 

278 

39 

8  1     <C7 

3i  8 

26  o 

108  2 

40 

81.40 

35-6 

152.0 

26.04 

30.1 

III.  2 

14-3 

274 

274 

41 

81.50 

33-8 

I5I-9 

25.9 

30.26 

.... 

•    •  •  • 

112.  2 

I5-I 

274 

274 

266 


ECONOMY   OF   STEAM-ENGINES 


Table  XXIV  gives  tests  made  on  this  engine  without  steam 
in  the  jackets  and  with  steam  supplied  to  the  tubular  reheaters; 
the  results  of  these  tests  will  be  discussed  later. 


TABLE  XXIV. 

TRIPLE-EXPANSION  EXPERIMENTAL  ENGINE  AT  THE  MASSA- 
CHUSETTS INSTITUTE  OF  TECHNOLOGY  WITH  TUBULAR 
REHEATERS. 


$ 

1 

Per  cent  of 

,| 

OH 

n;-§  . 

£ 

3  3 

§ 

8*0  >, 

a  ^ 

steam  used 

fe-d 

^•§  i 

Condition. 

•2£ 
2% 

ill 

tO    fl! 
2  §0 

I6 

efcfc 
3  g  s 

II 

in  reheaters 

f 

a 

^h 

a^ 

c  ^ 

si 

»-a    i 
S^ 

kjl 

M 

|'§ 

«F" 

1" 

3  ««*- 
> 

S"8 

m 

1 

1 

1 

ia 

hki 
pq 

S^ 

Without 

81  8 

146.  7 

26.4 

30.6 

88  6 

288 

steam  in 

81  8 

27 

147.5 

26.1 

30.4 

87.5 

16.0 

28 

reheaters 

81  6 

147.0 

25.9 

30.5 

89  7 

16  o 

28 

4 

8l.'2 

36 

148.2 

25-9 

30.2 

103.3 

15-5 

282 

28l 

S 

Steam  in 

85.5 

10 

147-2 

25.5 

30.0 

.... 

13 

66.5 

iS-7 

277 

273 

6 

first 

83.5 

19 

146.9 

23.8 

30.2 

14 

84.9 

iS-9 

277 

262 

7 

reheater. 

81.4 

31 

146.1 

25.8 

30.2 

.... 

12 

112.4 

15-0 

266 

264 

8 

85.0 

8 

147-3 

26.6 

30.3 

10 

7 

61.5 

iS-S 

269 

274 

9 

Steam  in 

84-5 

10 

146.9 

26.2 

30.3 

12 

8 

74-8 

14.9 

261 

260 

IO 

both 

82.4 

21 

147-1 

25-3 

30.4 

10 

6 

95-7 

14-7 

258 

252 

ii 

reheaters. 

81.9 

2? 

147-7 

25-4 

30.1 

6 

9 

105.9 

14.7 

259 

254 

12 

82.0 

28 

146.6 

25-7 

30.2 

7 

8 

107.0 

14-5 

256 

254 

Gain  from  Steam-jackets.  —  Much  of  the  difference  of  opinion 
concerning  the  advantage  to  be  derived  from  the  use  of  steam- 
jackets  is  to  be  ascribed  to  indiscriminate  comparison  of  tests 
on  various  engines,  or  to  the  failure  to  obtain  any  advantage 
from  jackets  which  were  not  applied  with  discrimination.  Should 
any  engine  when  properly  tested  and  computed,  show  no  advan- 
tage from  the  use  of  a  steam-jacket,  it  will  be  better  to  omit 
that  device  in  future  constructions  for  the  same  conditions 
unless  there  are  constructive  reasons  for  retaining  it. 

In  order  to  obtain  definite  conclusions  from  tests  made  to 
determine  the  advantage  of  the  use  of  steam-jackets,  such  tests 
should  be  made  in  definite  series  in  which  only  one  property  is 
varied  at  a  time,  and  from  these  tests  the  best  results  under 


GAIN   FROM   STEAM-JACKETS  267 

the  most  favorable  conditions  should  be  chosen  when  the  engine 
has  steam  in  the  jackets,  and  in  like  manner  the  best  result 
without  steam  in  the  jackets  should  be  selected;  a  comparison 
of  two  such  selected  tests  has  more  weight  than  a  haphazard 
comparison  of  individual  tests,  however  great  the  number  of 
such  tests  may  be.  An  investigation  of  Delafond's  tests  in 
Tables  XXI  and  XXII  and  represented  by  Figs.  57  and  58, 
gives  such  a  comparison.  The  tests  selected  are  those  given  in 
Table  X  and  give  two  pairs,  with  condensation  and  without. 
Thus  the  best  result  with  steam  in  the  jacket  and  with  conden- 
sation is  16.9  pounds,  and  without  steam  in  the  jacket  is  18.1; 
the  gain  is 

18.1  —  16.0 
y  =0.07. 

18.  i 

Without  condensation  the  best  results  are  21.5  with  steam  in 
the  jackets  and  24.2  without  steam  in  the  jackets;  the  gain  is 

24.2  —  21. s 

~ p  =  o.n. 

24.2 

These  results  are  probably  too  small,  as  the  steam  used  in  the 
jackets  should  be  collected  and  returned  to  the  boiler  with  only 
a  moderate  reduction  of  temperature  below  the  temperature  of 
the  steam  in  the  boiler.  The  drip  from  the  jackets  was  passed 
through  a  trap,  and  as  reported  is  probably  too  small,  this  being 
the  most  questionable  result  from  the  tests. 

Data  for  a  similar  comparison  for  compound  engines  are  not 
at  hand,  but  the  tests  described  on  page  265  seem  to  be  conclusive 
for  the  triple  engine. 

From  the  diagram  Fig.  59  the  best  results  with  steam  in  all 
the  jackets  of  the  cylinders  and  without  steam  in  any  of  the 
jackets  are  233  and  274  B.T.U.  per  horse-power  per  minute,  and 
the  gain  from  the  use  of  the  steam  in  the  jacket  is 

2 74  ~  233    x  I00  =  I5  per 
274 


268  ECONOMY    OF    STEAM-ENGINES 

These  heat-consumptions  correspond  to  13.8  and  15.2  pounds 
of  steam  per  horse-power  per  hour,  so  that  on  the  basis  of  steam- 
consumption  the  gain  from  the  use  of  steam  in  the  jackets  would 
appear  to  be  only  9  per  cent,  instead  of  the  actual  gain  of  1 5  per 
cent.  This  large  difference  is  due  to  the  large  percentage  of 
steam  used  in  the  jackets,  amounting  in  all  to  17  or  18  per  cent 
of  the  total  steam-consumption.  The  steam  used  in  an  indi- 
vidual jacket  is,  however,  not  excessive,  being  about  2.5  per  cent 
in  the  jackets  of  the  high-pressure  cylinder  and  7  or  8  per  cent  in 
the  jackets  of  each  of  the  other  two  cylinders. 

The  effect  of  jacketing  the  heads  of  the  cylinders  only  is 
surprisingly  small,  as  from  the  diagram  the  best  result  is  262 
B.T.U.  per '^horse-power  per  minute,  which  compared  with  the 
best  result  without  steam  in  any  of  the  jackets  gives  a  gain  of 
only 

274  —  262    , 

-J-L X  ioo  =  4  per  cent. 

274 

The  correspondence  between  this  result  and  the  experiments  by 
Callendar  and  Nicolson  on  the  action  of  the  cylinder  walls, 
has  already  been  pointed  out. 

From  the  tests  just  discussed  and  compared  it  appears  con- 
servative to  say  that  about  ten  per  cent  can  be  gained  by  using 
steam-jackets  on  simple  and  compound  engines  and  that  fifteen 
per  cent  can  be  gained  by  their  use  on  triple-expansion  engines; 
provided  that  these  conclusions  shall  not  be  applied  to  engines  of 
more  than  300  horse-power.  The  saving  on  massive  engines 
of  1000  horse-power  or  more  is  likely  to  be  smaller,  and  very 
large  engines  may  derive  no  benefit  from  steam-jackets.  On 
the  other  hand,  a  saving  of  25  per  cent  may  be  obtained  from 
jackets  on  small  engines  of  five  or  ten  horse-power.  Such  trivial 
engines  are  never  provided  with  jackets  unless  for  experimental 
purposes,  and  the  results  of  such  experiments  are  of  little  value. 

Intermediate  Reheaters.  —  Many  compound  and  triple- 
expansion  engines  have  some  method  of  reheating  the  steam 
on  its  way  from  one  cylinder  to  another.  Notable  examples 


INTERMEDIATE    REHEATERS  269 

are  the  Leavitt  pumping-engines,  for  which  results  are  given  in 
Table  X.  The  fact  that  these  engines  give  the  best  economies 
recorded  for  engines  using  saturated  steam  lead  to  the  inference 
that  such  reheaters  may  be  used  to  advantage.  The  only  direct 
evidence,  however,  is  not  so  favorable,  for,  as  has  been  pointed 
out  on  page  264,  there  was  found  a  small  but  distinct  disadvantage 
from  using  steam  in  double  walls  or  jackets  on  the  intermediate 
receivers  of  the  experimental  engine  at  the  Massachusetts  Institute 
of  Technology.  It  appears  that  this  engine  gives  the  best 
economy  when  steam  is  supplied  to  the  jackets  on  the  cylinders 
and  not  to  the  jackets  on  the  reheaters,  and,  further,  that  when 
steam  is  used  in  the  receiver-jackets  the  steam  in  the  low- 
pressure  cylinder  shows  signs  of  superheating,  which  may  be 
considered  to  indicate  that  the  use  of  the  steam-jacket  is  carried 
too  far. 

After  the  tests  referred  to  were  finished  the  engine  was  fur- 
nished with  reheaters  made  of  corrugated-copper  tubing,  so 
arranged  that  one-third,  two-thirds,  or  all  of  the  reheating-surface 
can  be  used,  when  desired.  Table  XXIV,  page  266,  gives  the 
results  of  tests  made  on  the  engine  with  and  without  steam  in 
the  reheaters;  in  these  tests  the  entire  reheating-surface  was  used 
when  steam  was  supplied  to  a  reheater. 

For  some  reason  the  heat-consumption  when  no  steam  was 
used  in  the  reheaters  is  somewhat  greater  than  that  given  in 
Table  XXIV  for  the  engine  without  steam  in  any  of  the 
jackets;  the  difference,  however,  is  not  more  than  two  or  two 
and  a  half  per  cent  and  cannot  be  considered  of  much  importance. 
It  is  clear  from  the  table  that  there  is  advantage  from  using  one 
reheater,  and  still  more  from  using  two.  If  the  heat-consumption 
for  the  engine  without  steam  in  the  jackets  and  without  steam 
in  the  reheaters  (taken  from  Table  XXIV)  is  assumed  to  be 
274  B.T.U.  per  minute,  then  the  gain  from  using  the  reheaters 
appears  to  be 


x  ioo  =  8  per  cent, 


274 


270  ECONOMY    OF    STEAM-ENGINES 

which  is  scarcely  more  than  half  the  gain  from  using  steam  in 
the  jackets.  These  tests  cannot  be  considered  conclusive,  as 
they  are  too  few  and  refer  only  to  one  engine. 
.  Superheating.  —  The  most  direct  and  effective  way  of  reducing 
the  interference  of  the  cylinder  walls  and  of  improving  steam- 
engine  economy  is  by  the  use  of  superheated  steam.  About 
1863-64  a  number  of  naval  vessels  were  supplied  with  super- 
heaters by  Chief  Engineer  Isherwood,  and  when  tested  by  him 
showed  a  marked  advantage  which  led  to  the  adoption  of  super- 
heated steam  for  stationary  and  marine  practice  both  in  America 
and  in  Europe.  But  the  superheaters  which  were  exposed  to 
dry  steam  on  one  side  and  to  the  flue  gases  on  the  other,  rapidly 
deteriorated,  and  after  an  experience  lasting  ten  or  fifteen  years 
the  use  of  superheated  steam  was  abandoned  in  favor  of  com- 
pound and  triple  engines  with  high-pressure  steam. 

More  recently  improved  forms  of  superheaters  have  been 
introduced  in  Great  Britain  and  Germany,  which  show  good 
endurance,  and  superheated  steam  appears  to  have  been  used 
successfully  for  sufficient  times  to  warrant  the  conclusion  that 
the  application  of  superheated  steam  has  been  accomplished. 
Two  series  of  tests  will  be  discussed,  namely,  some  early  tests 
on  a  simple  engine,  and  some  recent  tests  on  compound  engines. 
There  appears  to  be  no  reason  for  extending  the  application  of 
superheated  steam  to  triple  engines. 

Dixwell's  Tests. — A  small  Harris- Corliss  engine  was  fitted 
up  for  making  tests  on  superheated  steam  at  the  Massachusetts 
Institute  of  Technology  by  Mr.  George  B.  Dixwell.  Six  tests 
with  superheated  and  saturated  steam  were  made  on  this  engine 
in  1877  in  the  presence  of  a  board  of  engineers  of  the  United 
States  Navy. 


DIX WELL'S   TESTS 


27I 


TABLE  XXV. 

DIXWELL'S   TESTS   ON    SUPERHEATED   STEAM. 

CYLINDER   DIAMETER   8   INCHES;    STROKE    2    FEET. 

Proceedings  of  the  Society  of  Arts,  Mass.  Inst.  Tech.,  1887-88. 


Saturated  Steam. 

Superheated  Steam. 

I 

II 

III 

IV 

V 

VI 

75 
0.672 
59-5 

50.2 
15-5 

406 
315 

8.9 
ii.  5 
15-63 
35-8 
621 

Duration,  minutes   .       .    .       

127 
0.217 
61.5 

50.4 
iS-4 

302 
278-297 

52-2 
32.4 
7.65 
48.2 
796 

83 
0-443 
60.4 

50.2 

15-7 

303 
279-296 

35-9 
29-3 
12.7 
42.2 
696 

63 
0.689 
58.0 

50.3 
15-8 

303 
282-300 

27.9 
23-9 
15.68 
45-3 

747 

180 
0.218 
61.0 

50.4 
15-2 

478 
3i3 

27.4 
18.3 
6.83 
35-2 
631 

108 
0.439 
61.4 

50.0 
15-4 

441 
316 

13-6 
13-6 
12.37 
31-7 

546 

Cut-off                                                        . 

Revolutions  per  minute  

Boiler-pressure  above  atmosphere,  pounds 
per  square  inch    
Back-pressure,  absolute,  pounds  per  sq.  in. 
Temperatures  Fahrenheit: 

In  cylinder  by  pyrometer    
Per  cent  of  water  in  cylinder: 
At  cut-off 

At  end  of  stroke 

Horse-power     

Steam  per  horse-power  per  hour,  pounds, 
B.T.U.  per  horse-power  per  minute.    .    . 

A  metallic  thermometer  or  pyrometer  was  placed  in  a  recess 
in  the  head  of  the  cylinder.  When  saturated  steam  was  used 
this  pyrometer  showed  a  large  fluctuation,  but  when  superheated 
steam  was  used  its  needle  or  indicator  was  at  rest.  Even  if  a 
part  of  the  apparent  change  of  temperature  with  saturated  steam 
is  attributed  to  the  vibration  of  the  needle  and  the  multiplying 
mechanism,  it  is  very  clear  that  the  use  of  superheated  steam 
reduces  the  change  of  temperature  of  the  cylinder-head  in  a 
remarkable  manner.  The  effect  of  superheating  on  the  action 
of  the  cylinder  walls  is  also  indicated  by  the  per  cent  of  water 
in  the  cylinder  at  cut-off  and  release. 

The  apparent  gain  by  comparing  the  amounts  of  steam  used 
per  horse-power  per  hour  in  favor  of  superheated  steam  is  but 


42.2  -  31.7 
42.2 


X  ioo  =  25  per  cent; 


this  result  is  of  course  misleading,  since  the  superheating  required 
additional  coal.     As  the  coal-consumption  was  not  determined, 


272  ECONOMY   OF   STEAM-ENGINES 

we  must  compare  instead  the  B.T.U.  per  horse-power  per  minute, 
giving  a  real  gain  of 

606  —  546    , 

-*  —  ,  /        X  100  =  IQ  per  cent. 
696 

This  same  Harris-  Corliss  engine  afterwards  showed  a  heat- 
consumption  of  548  B.T.U.  per  horse-power  per  minute  when 
supplied  with  saturated  steam  at  77  pounds  pressure,  which  shows 
why  the  earlier  attempts  at  the  use  of  superheated  steam  were 
so  easily  set  aside  when  it  was  found  expedient  to  raise  the  steam- 
pressure. 

Though  we  have  no  tests  with  high-pressure  steam  and  with 
condensation  on  engines  of  two  or  three  hundred  horse-power, 
it  is  probable  that  a  very  material  saving  could  be  made  by  the 
use  of  superheated  steam  under  such  conditions;  if  the  saving  in 
heat  were  as  much  as  fifteen  per  cent,  it  would  reduce  the  steam- 
consumption  to  a  larger  degree,  perhaps  by  twenty  per  cent, 
and  would  be  likely  to  give  from  14.5  to  15  pounds  of  superheated 
steam  per  horse-power  per  hour. 

The  best  results  obtained  from  the  application  of  superheated 
steam  in  compound  engines  are  reported  by  Professor  Schroter, 
in  Table  XXVI,  for  a  tandem-engine  with  poppet-valves 
built  in  Ghent.  Five  tests  were  made  with  varying  cut-off  and 
with  saturated  steam,  and  five  others  also  with  varying  cut-off 
and  with  steam  that  was  superheated  about  250°  F.,  the  absolute 
initial  pressure  in  the  cylinder  being  about  145  pounds,  so  that 
the  boiler-pressure  was  probably  between  130  and  135  pounds  by 
the  gauge. 

This  engine  gave  a  remarkable  economy  both  with  saturated 
steam  and  with  superheated  steam,  its  steam  and  heat-consump- 
tion being  only  five  per  cent  more  than  that  of  the  triple-expansion 
Leavitt  engine  recorded  in  Table  X.  The  gain  from  using 
superheated  steam  appears  to  be 


=  0.06. 
213 


SCHROTER   TESTS 


273 


which  places  it  a  little  beyond  the  performance  of  the  triple 
engine  mentioned.  But  since  the  uncertainty  of  the  determina- 
tion of  power  by  the  indicator  is  probably  two  per  cent,  we  may 
reasonably  conclude  that  the  effect  of  using  superheated  steam 
in  a  compound  engine  is  to  place  it  on  a  level  with  a  triple 
engine,  and  the  question  is  to  be  decided  in  practice  by  the 
relative  expense  and  trouble  of  supplying  and  using  a  superheater 
instead  of  a  third  cylinder  and  higher  steam-pressure. 

It  is  somewhat  remarkable  that  steam  was  supplied  to  the 
jackets  during  the  superheating  tests,  but  not  at  all  surpris- 
ing that  for  those  tests  the  jackets  had  a  small  effect,  as  is 
made  evident  by  noting  the  percentages  of  steam  condensed  in 
them. 

TABLE  XXVI. 

COMPOUND    HORIZONTAL   MILL-ENGINE. 

CYLINDER    DIAMETERS    12.8    AND    22    INCHES;    STROKE    33.5    INCHES. 

By   Professor   M.     SCHROTER,    Mitleilungen    tiber    Forschungsarbeiten, 
Heft  19,  1904. 


Saturated. 

Superheated. 

I 

II 

III 

IV 

V 

VI 

VII 

VIII 

IX 

X 

Horse-power    

299 

26^ 

211 

1  60 

112 

303 

258 

112 

161 

Duration,  minutes  

60 

61 

57-5 

55 

5° 

48 

60 

51 

64.5 

55 

Revolutions  per  minute      

126 

126 

126.5 

127 

128 

126 

126 

126.5 

127 

T78 

Cut-off,  high-pressure  cylinder      .    . 

0.^8 

0.31 

O.22 

0.15 

0.10 

0.41 

0.33 

O.26 

0.16 

0.10 

Total  expansions     
Initial  pressure,  absolute  pounds  per 

7-9 

9-7 

13-5 

20 

30 

7-3 

9-i 

ii.  5 

18.7 

30 

am  
-pressure,  absolute   pounds  per 

148 

146 

147 

141 

142 

148 

149 

149 

I46 

146 

sq.m  

1-3 

i  .  i 

I  .  I 

I  .  I 

1.  1 

i  .3 

i  .0 

1.  1 

Superheating,  degrees  F  
Steam    per    horse-power  per    hour, 

246 

257 

258 

256 

256 

pounds  .    .    . 

13-6 
10.9 
246 
0.901 

12.8 

ii.  8 
232 
0.891 

12.3 
12.9 
222 
0.872 

ii.  8 
13-7 
213 
0.842 

12 
14.4 

216 

0.786 

10.9 

2.1 
223 
0.002 

10.4 
3-5 
215 
0.890 

10 

3-8 
206 

0.872 

9-7 
4-4 

201 

0.842 

9.6 
4.6 
199 
0.790 

Per  cent  condensed  in  jackets  .    .    . 
B.T.U.  per  horse-power  per  min. 
Mechanical  efficiency     

Cut-off  and  Expansion.  —  It  has  already  been  pointed  out  on 
page  256  in  connection  with  Delafond's  tests  that  the  best  point 
of  cut-off  for  a  simple  engine,  whether  jacketed  or  not,  is  about 


274  ECONOMY    OF   STEAM-ENGINES 

one-third  stroke  when  the  engine  is  non-condensing,  and  it  is 
about  one-sixth  stroke  when  condensing.  In  general,  other 
tests  on  simple  engines  such  as  those  on  the  Gallatin,  and  on 
the  small  Corliss  engine  at  the  Massachusetts  Institute  of 
Technology,  confirm  these  conclusions. 

The  term  total  expansion  for  a  compound  or  a  triple  engine 
can  properly  have  only  a  conventional  significance;  it  is  usually 
taken  to  be  the  product  of  the  ratio  of  the  large  to  the  small 
cylinder  by  the  reciprocal  of  the  fraction  of  the  stroke  at  cut-off 
for  the  high- pressure  cylinder.  This  conventional  total  expan- 
sion is  about  20  for  all  the  tests  on  triple  engines  quoted  in  Table 
X,  except  those  on  marine  engines,  which  show  a  relatively 
poor  economy.  It  may  therefore  be  concluded  that  it  is  not 
advisable  to  use  much  more  expansion  for  any  triple  engine, 
and  that  less  expansion  should  be  used  only  when  the  condi- 
tions of  service  (for  example,  at  sea)  prevent  the  use  of  large 
expansion. 

The  stationary  compound  engines  given  in '  Table  X  also 
have  about  20  expansions,  and  experience  shows  conclusively 
that  for  highest  economy  such  a  degree  of  expansion  is  re- 
quired. In  practice  somewhat  less  may  frequently  be  found 
advisable. 

Variation  of  Load.  —  In  general,  an  engine  should  be  so 
designed  that  it  may  give  a  fair  economy  for  a  considerable 
range  of  load  or  power.  Very  commonly  the  engine  will  have 
sufficient  range  of  power  with  good  economy  if  designed  to  give 
the  best  economy  at  the  normal  load.  In  general,  however, 
it  is  well  to  assign  a  less  expansion  and  consequently  a  longer 
cut-off  to  the  engine  than  would  be  determined  from  a  con- 
sideration of  the  steam-  (or  heat-)  consumption  alone.  For, 
in  the  first  place,  the  best  brake  or  dynamic  economy  is  always 
attained  for  a  little  longer  cut-off  than  that  which  gives  the 
best  indicated  economy,  and  in  the  second  place  the  economy 
is  less  affected  by  lengthening  than  by  shortening  the  cut-off. 
The  first  comes  from  the  fact  that  the  frictional  losses  of  the 
engine  increase  less  rapidly  than  the  power,  as  will  be  shown 


VARIATION    OF   LOAD  275 

in  the  next  chapter;  and  the  second  is  evident  from  consideration 
of  curves  of  steam-consumption  as  given  by  Fig.  59,  page  262, 
and  Figs.  57  and  58,  pages  252-253. 

The  allowable  range  of  power  for  a  simple  engine  is  greater 
than  for  a  compound  or  a  triple  engine.  Comparisons  for  a 
simple  and  a  triple  engine  may  be  made  by  aid  of  Figs.  58  and 
59.  The  Corliss  engine  at  Creusot  when  supplied  with  steam 
at  60  pounds  pressure,  with  condensation  and  with  steam  in 
the  jacket,  developed  150  horse-power  and  used  17.3  pounds 
of  steam  per  horse-power  per  hour.  If  the  increase  be  limited 
to  10  per  cent  of  the  best  economy,  that  is,  to  19  pounds  per 
horse-power  per  hour,  the  horse-power  may  be  reduced  to  about 
92,  giving  a  reduction  of  nearly  40  per  cent  from  the  normal 
power.  The  triple  engine  at  the  Massachusetts  Institute  of 
Technology  with  steam  at  150  pounds  pressure  and  using  steam 
in  all  the  cylinder- jackets  developed  140  horse-power  and  used 
233  B.T.U.  per  horse-power  per  minute.  Again,  limiting  the 
increased  consumption  to  10  per  cent  or  to  254  B.T.U.,  the  power 
may  be  reduced  to  about  104  horse-power,  giving  a  reduction  of 
26  per  cent  from  the  normal  power.  The  effect  of  increasing 
power  for  these  engines  cannot  be  well  shown  from  the  tests 
made  on  them,  but  there  is  reason  to  believe  that  the  simple 
engine  would  preserve  its  advantage  if  a  comparison  could  be 
made.  Though  the  tests  which  we  have  on  compound  engines 
do  not  allow  us  to  make  a  similar  investigation  of  the  effect  of 
changing  load,  there  is  no  doubt  that  it  is  intermediate  in  this 
respect  between  the  simple  and  the  triple  engine. 

When  the  power  developed  by  a  compound  engine  is  reduced 
by  shortening  the  cut-off  of  the  high-pressure  cylinder,  the  cut-off 
of  the  low-pressure  cylinder  must  be  shortened  at  the  same  time 
to  preserve  a  proper  distribution  of  power  and  division  of  the 
range  of  temperature  between  the  cylinders.  If  this  is  not  done 
the  work  will  be  developed  mainly  in  the  high-pressure  cylinder, 
which  will  be  subjected  to  a  large  fluctuation  of  temperature, 
and  the  engine  will  lose  the  advantages  sought  from  compounding. 
A  compound  non-condensing  engine,  if  the  cut-off  for  the  large 


276  ECONOMY   OF   STEAM-ENGINES 

cylinder  is  fixed,  is  likely  to  have  a  loop  on  the  low-pressure 
indicator-diagram  due  to  expansion  below  the  atmosphere,  if 
the  power  is  reduced  by  shortening  the  cut-off  of  the  high- pressure 
cylinder.  Such  a  loop  is  always  accompanied  by  a  large  loss  of 
economy;  if  the  loop  is  large  the  engine  may  be  more  wasteful 
than  a  simple  engine,  for  the  high-pressure  piston  develops 
nearly  all  the  power  and  may  have  to  drag  the  low-pressure 
piston,  which  is  then  worse  than  useless. 

There  is  seldom  much  difficulty  in  running  a  simple  engine  at 
any  desired  reduced  power  by  shortening  the  cut-off  or  reducing 
the  steam-pressure,  or  by  a  combination  of  the  two  methods. 
But  a  compound  engine  sometimes  gives  trouble  when  run  at 
very  low  power  (even  when  attention  is  given  to  the  cut-off  of 
the  low-pressure  cylinder),  which  usually  takes  the  form  just 
discussed;  i.e.,  the  power  is  developed  mainly  in  the  high-pressure 
cylinder.  Triple  engines  are  even  more  troublesome  in  this 
way.  A  compound  or  triple  engine  running  at  much  reduced 
power  is  subject  not  only  to  loss  of  economy  and  to  irregular 
action,  but  the  inside  surface  of  the  low-pressure  cylinder  is 
liable  to  be  cut  or  abraded. 

Automatic  and  Throttle  Engines.  —  The  power  of  an  engine 
may  be  regulated  by  (i)  controlling  the  steam- pressure,  or  (2) 
by  adjusting  the  cut-off.  Usually  these  two  methods  are  used 
separately,  but  in  some  instances  they  are  used  in  combination. 
Thus  a  locomotive-driver  may  reduce  the  power  of  his  engine 
either  by  shortening  the  cut-off  or  by  partially  closing  the  throttle- 
valve,  or  he  may  do  both  at  once.  Stationary  engines  are  usually 
run  at  a  fixed  speed  and  are  controlled  by  mechanical  governors, 
which  commonly  consist  of  revolving  weights  that  are  urged 
away  from  the  axis  of  revolution  by  centrifugal  force  and  are 
restrained  by  the  attraction  of  gravity  or  by  the  tension  of 
springs. 

The  earliest  and  simplest  steam-engine  governor,  invented  by 
Watt,  has  a  pair  of  revolving  pendulums  (balls  on  the  ends  of 
rods  that  are  hinged  to  a  vertical  spindle  at  their  upper  ends) 
which  are  urged  out  by  centrifugal  force  and  are  drawn  down 


AUTOMATIC   AND   THROTTLE   ENGINES  277 

by  gravity.  When  the  engine  is  running  steadily  at  a  given 
speed  the  forces  acting  on  the  governor  are  in  equilibrium  and 
the  balls  revolve  in  a  certain  horizontal  plane.  If  the  load  on 
the  engine  is  reduced  the  engine  speeds  up  and  the  balls  move 
outward  and  upward  until  a  new  position  of  equilibrium  is 
found  with  the  balls  revolving  in  a  higher  horizontal  plane. 
Through  a  proper  system  of  links  and  levers  the  upward  motion 
of  the  balls  is  made  to  partially  close  a  throttle- valve  in  the  pipe 
which  supplies  steam  to  the  engine  and  thus  adjusts  the  work  of 
the  engine  to  the  load. 

Shaft-governors  have  large  revolving- weights  whose  centrifugal 
forces  are  balanced  by  strong  springs.  They  are  powerful 
enough  to  control  the  distribution  or  the  cut-off  valve  of  the 
engine,  which,  however,  must  be  balanced  so  that  it  may  move 
easily. 

Automatic  engines,  like  the  Corliss  engines,  have  four  valves, 
two  for  admission  and  two  for  exhaust  of  steam.  The  admission, 
release,  and  compression  are  fixed,  but  the  cut-off  is  controlled 
by  the  governor.  Usually  an  admission- valve  is  attached  to  the 
actuating  mechanism  by  a  latch  or  similar  device,  which  can  be 
opened  by  the  governor,  and  then  the  valve  is  closed  by  gravity 
by  a  spring,  or  by  some  other  independent  device.  The  office 
of  the  governor  is  to  control  the  position  of  a  stop  against 
which  the  latch  strikes  and  by  which  it  is  opened  to  release  the 
valve. 

Corliss  and  other  automatic  engines  have  long  had  a  deserved 
reputation  for  economy,  which  is  commonly  attributed  to  their 
method  of  regulation.  It  is  true  that  the  valve-gears  of  such 
engines  are  adapted  to  give  an  early  cut-off,  which  is  one  of  the 
elements  of  the  design  of  an  economical  simple  engine,  but  their 
advantage  over  some  other  engines  is  to  be  largely  attributed 
to  the  small  clearance  which  the  use  of  four  valves  makes  con- 
venient, and  to  the  fact  that  the  exhaust-steam  is  led  immediately 
away  from  the  engine,  without  having  a  chance  to  abstract  heat 
after  it  leaves  the  cylinder.  These  engines  also  are  free  from 
the  loss  which  Callendar  and  Nicolson  attribute  to  direct  leakage 


278  ECONOMY    OF    STEAM-ENGINES 

from  the  steam  to  the  exhaust  side  of  slide-valves,  and  to  valves 
of  similar  construction. 

Every  steam-engine  should  have  a  reserve  of  power  in  excess 
of  its  normal  power;  and  again  it  is  convenient  if  not  essential 
that  a  single-cylinder  engine  should  be  able  to  carry  steam 
through  the  greater  part  of  its  stroke  in  starting.  These  condi- 
tions, together  with  the  fact  that  it  is  somewhat  difficult  to  design 
a  plain  slide-valve  engine  to  give  an  early  cut-off,  have  led  to  the 
use  of  a  long  cut-off  for  engines  controlled  by  a  throttle-governor. 
The  tests  on  the  Corliss  engine  at  Creusot  (Tables  XXI  and 
XXII,  pp.  250  and  251)  show  clearly  the  disadvantage  of  using 
a  long  cut-off  for  simple  engines.  It  has  already  been  pointed 
out  that  a  non-condensing  engine  should  have  the  cut-off  at 
about  one-  third  stroke.  With  cut-off  at  that  point  and  with  75 
pounds  steam-pressure  the  engine  developed  209  horse-power 
and  used  24.2  pounds  of  steam  per  horse-power  per  hour  when 
running  without  steam  in  the  jacket  and  without  condensation. 
If  the  steam-pressure  is  reduced  to  50  pounds  and  the  cut-off  is 
lengthened  to  58  per  cent  of  the  stroke,  the  steam-consumption 
is  increased  to  30.2  pounds  per  horse-power  per  hour,  the  horse- 
power being  then  173.  The  gain  from  using  the  shorter  cut- 
off is 

30.2  —  24.2 

^  -  X  100  =  20  per  cent. 
30.2 

A  similar  comparison  for  the  same  engine  running  with  a 
vacuum  and  with  steam  in  the  jacket  shows  even  a  larger  differ- 
ence. Thus  in  test  16  the  steam-  pressure  is  84  pounds  and  the 
cut-off  is  at  11.5  per  cent  of  the  stroke,  the  horse-power  is  176, 
and  the  steam-consumption  per  horse-power  per  hour  is  16.9 
pounds,  while  the  consumption  for  about  the  same  power  in  test 
44  is  25.4  pounds  of  steam  per  horse-power  per  hour,  the  steam- 
pressure  being  35  and  the  cut-off  at  58  per  cent  of  the  stroke; 
here  the  gain  from  using  the  shorter  cut-off  is 

2<.A   —   l6. 


25.4 


X  ioo  =  33  per  cent. 


EFFECT    OF    SPEED    OF    REVOLUTION  279 

Considering  also  that  automatic  engines  are  usually  well 
built  and  carefully  attended  to,  while  throttling-engines  are 
often  cheaply  built  and  neglected,  the  good  reputation  of 
the  one  and  the  bad  reputation  of  the  other  are  easily  ac- 
counted for. 

It  is,  however,  far  from  certain  that  an  automatic  engine  will 
have  a  decided  advantage  over  a  throttle-engine,  provided  the 
latter  is  skilfully  designed,  well  built  and  cared  for,  and  arranged 
to  run  at  the  proper  cut-off.  Considering  the  rapid  increase  in 
steam-consumption  per  horse-power  per  hour  when  the  cut-off 
is  unduly  shortened,  it  is  not  unreasonable  to  expect  as  good  if 
not  better  results  from  a  simple  throttling-engine  than  from  an 
automatic  engine  when  both  are  run  for  a  large  part  of  the  time 
at  reduced  power. 

The  disadvantage  of  running  a  compound  or  a  triple  engine 
with  too  little  expansion  can  be  seen  by  comparing  the  steam- 
consumptions  of  marine  and  stationary  engines;  on  the  other 
hand,  the  great  disadvantage  of  too  much  expansion  is  made 
evident  from  the  tests  on  the  engine  in  the  laboratory  of  the 
Massachusetts  Institute  of  Technology  (Table  XXIII,  page 
265).  Considering  that  the  allowable  variation  from  the  most 
economical  cut-off  is  more  limited  for  a  compound  or  a  triple 
engine,  it  appears  that  there  is  less  reason  for  using  an  automatic 
governor  instead  of  a  throttling  governor  for  compound  and 
triple  engines  than  there  is  with  simple  engines.  Nevertheless 
the  most  economical  engines  (simple,  compound,  or  triple)  are 
automatic  engines. 

Effect  of  Speed  of  Revolution.  —  Though  the  condensation  of 
steam  on  the  walls  of  the  cylinder  of  a  steam-engine  is  very 
rapid,  it  is  not  instantaneous.  It  would  therefore  appear  that 
an  improvement  in  economy  might  be  attained  by  increasing  the 
number  of  revolutions  per  minute;  but  whatever  might  be  thus 
gained  is  more  than  offset  by  the  increase  of  the  dimensions  of 
valves,  passages,  and  clearances  that  would  accompany  such  a 
change  in  speed,  for  it  has  already  been  pointed  out  that  the  evil 
of  initial  condensation  is  much  aggravated  by  increasing  the 


28o  ECONOMY   OF    STEAM-ENGINES 

surfaces  exposed  to  steam  in  clearance  spaces.  As  a  matter  of 
fact,  all  engines  which  for  various  reasons  have  been  designed 
to  run  at  very  high  rotative  speeds  have  shown  relatively  poor 
economy,  in  part  from  the  reason  given,  and  in  part  from  the 
fact  that  piston-valves  are  commonly  used,  and  they  are  subject 
to  the  kind  of  leakage  described  by  Callendar  and  Nicolson  on 
page  234,  even  when  they  are  in  good  condition.  Very  com- 
monly the  engine  has  a  fly-wheel  governor,  which  requires  the 
valve  to  be  very  free  with  the  chance  of  excessive  leakage.  Mr. 
Willans  invented  a  single-acting  triple-expansion  engine  to  run 
at  high  rotative  speed,  and  succeeded  in  getting  abundant  steam- 
passages  without  excessive  clearances  by  using  a  hollow  piston- 
rod  to  carry  the  steam  from  cylinder  to  cylinder,  all  arranged 
tandem.  Tests  on  this  engine  (which  are  not  quoted  elsewhere 
in  this  book)  showed  that  an  increase  from  100  revolutions  to 
200  revolutions  per  minute  reduced  the  steam-consumption 
from  24.7  to  23.1  pounds  per  horse-power  per  hour,  and  a 
further  increase  of  speed  to  400  revolutions  gave  a  reduction 
to  21.4  pounds;  the  engine  was  then  running  compound  non- 
condensing.  This  engine  used  12.7  pounds  of  steam  per  horse- 
power per  hour,  when  developing  30  horse- power,  at  380  revo- 
lutions per  minute  under  170  pounds  gauge-pressure,  acting  as 
a  triple-expansion  condensing  engine. 

Binary  Engine.  —  On  page  180,  under  the  subject  "  Compound 
Engines,"  attention  was  called  to  the  possibility  of  extending  the 
range  of  temperature  for  vapor-engines  by  the  use  of  two  fluids; 
the  second  fluid  (for  example,  sulphur  dioxide)  being  chosen  so 
that  a  good  working  back-pressure  could  be  maintained  at  the 
temperature  of  the  available  condensing  water  which  acts  as 
the  refrigerator  for  the  combined  engines.  Considering  only 
the  efficiency  of  Carnot's  cycle  for  the  customary  range  of 
temperature  for  a  steam-engine,  and  the  efficiency  for  the 
extended  range,  it  appeared  that  a  gain  of  20  per  cent  might 
be  possible. 

Recent  investigations  by  Professor  Josse  on  an  experimental 
engine  in  the  laboratory  of  the  Technical  High  School  at  Char- 


BINARY    ENGINE  281 

lottenburg  give  some  insight  into  the  possibilities  of  this  method. 
The  engine  is  of  moderate  size,  developing  about  1 50  horse-power 
as  a  steam-engine,  and  about  200  horse-power  as  a  binary  engine, 
using  steam  at  about  160  pounds  by  the  gauge  with  200°  F., 
superheating.  The  engine  is  a  three-cylinder  triple- expansion 
engine,  but  can  be  run  also  as  a  compound  engine,  though  it 
probably  is  not  proportioned  to  give  the  best  economy  under  the 
latter  condition. 

The  general  arrangement  of  the  engine  is  as  follows:  the  three 
steam-cylinders  are  arranged  horizontally  side  by  side,  and  the 
additional  cylinder  using  the  volatile  fluid  (sulphur  dioxide)  lies 
on  the  opposite  side  of  the  crank-shaft,  to  which  it  is  connected  by 
its  own  crank  and  connecting-rod.  Steam  is  supplied  from  the 
boiler  and  superheater  to  the  steam-engine,  and  is  exhausted 
into  a  tubular  condenser  which  acts  as  the  sulphur  dioxide 
vaporizes;  the  condensed  steam  is  pumped  back  into  the  boiler, 
and  the  vacuum  is  maintained  by  an  air-pump  as  usual;  a  vacuum 
of  20  to  25  inches  of  mercury  was  maintained  in  this  condenser. 
The  vaporous  sulphur  dioxide  at  a  pressure  of  120  to  180  pounds 
by  the  gauge  was  led  to  the  proper  cylinder,  from  which  it  was 
exhausted  at  about  35  pounds  by  the  gauge;  this  exhaust  was 
condensed  in  a  tubular  condenser  by  circulating  water  with  a 
temperature  of  about  50°  F.  at  the  inlet  and  about  65°  F.  at 
the  exit. 

The  drips  from  the  steam-jackets  of  the  steam-cylinders  were 
piped  to  the  steam-condenser  instead  of  being  returned  to  the 
boiler,  but  that  cannot  be  of  much  importance  because  the 
condensation  in  the  jackets  was  probably  less  than  five  per  cent 
of  the  total  steam  supplied  to  the  engine.  The  performance  of 
the  engine  is  given  in  Table  XXVIII  in  terms  of  steam  per 
horse-power  per  hour  and  in  thermal  units  per  horse-power  per 
minute;  the  latter  I  have  calculated  from  the  total  heat  of  the 
steam  including  the  superheat,  and  the  heat  of  the  liquid  at 
the  vacuum  in  the  steam-condenser.  Comparisons  must  be 
made  in  terms  of  thermal  units  in  order  to  take  account  of 
the  superheating. 


282 


ECONOMY   OF   STEAM-ENGINES 


TABLE  XXVII  . 

BINARY   ENGINE,   STEAM  AND    SULPHUR  DIOXIDE'. 
By  Professor  E.  JOSSE,  Royal  Technical  High  School,  Charlottenburg. 


Triple  Expansion. 

Com- 
pound. 

i 

2 

3 

4 

5 
145 

156.5 
23-8 

6 

7 
148 

156.5 
20.5 

8 

9 
137 

165.3 

21.8 

257 

121.  8 

13.5 
271 

178 

33 
152.8 

64.6 

50.2 
61.2 
48.0 
39-4 

169.8 
9-7 

4'i 

10 

148 

163.7 
20.7 
247 
140.5 
13-4 
266 

183 
35 

155-4 

66.9 
50.2 
63.3 
55-6 
39-5 

196.1 
9.6 
191 
9* 

Revolutions  per  minute      

Steam-Engine: 
Pressure    at    inlet,    h.p.   cylinder 
by  gauge  pounds     
Vacuum,  inches  of  mercury  .    .    . 
Superheating,  degrees  Fahrenheit 
Horse-power,  indicated  
Steam  per  h.p.  per  hour,  pounds  . 
Thermal  units  per  h.p.  per  minute 
Sulphur-Dioxide  Engine  : 
Pressure  by  gauge  pounds:    .    .    . 
In  vaporizer     

139.6 

136.5 
23-  Q 
175 
132.1 
12.5 
244 

132 
31 

132.0 

66.2 
49.6 
59-0 
45-3 
34-4 

177-4 
9-7 
i83 
85.5 

136.3 

156.5 
24-1 
219 
125.2 
II.  2 
223 

128 

34 
133-7 

65.8 
49-9 
60.2 
42.8 
34-2 

168 
8.36 
167 
86.2 

143-5 

158 
20.9 

137-4 

156.5 
25-4 

145 
156.5 

20.6 

149 

165.3 
20.4 

156.3 
16.4 
283 

181 
38 

153-5 

70.0 
50.2 
65.1 
66.0 
42.1 

222.3 
ii-S 
205 
90.5 

154-2 

12.  2 

240 

172 

35 
I5I.7 

67.6 
49-9 
62.4 
56.8 
37-0 

211 

8.9* 
176 
83.8 

101.6 
14.4 
289 

in 

3i 

123.7 

64.4 

50.2 
60.2 

31.0 
30.3 

132.6 
11.05 

215 

87.5 

145-3 
13-6 

270 

142 
36 

137-3 
68.5 

63  is 

50.1 
34-5 

195-4 

10.12 
200 

89.1 

144.5 

13.8 

270 

188 
36 

I57-I 

67.6 
50.2 
63.8 
57-6 
40.0 

202.1 
9.86 

193 

87 

161.0 
13-2 
261 

186 
36 

I55-I 

68.0 
50.2 
63-4 
61.  3 
37-9 

223.2 
9-55 
189 
90.8 

In  condenser    
Temperature  Fahr.  at  inlet  to  cyl- 

Temperature  Fahr.  at  outlet  from 
condenser     r  .    . 
of  circulating  water  inlet    .    ,  . 
outlet  .    :    . 
Horse-power,  indicated  

per  cent  of  steam-engine  power 
Combined  Engine: 
Horse-power,  indicated  ... 

Steam  per  h.p.  per  hour,  pounds  . 
Thermal  units  per  h.p.  per  minute 
Mechanical  efficiency      

Before  comparing  the  results  of  these  tests  to  determine  the 
gain  from  working  binary,  it  is  interesting  to  see  that  the  increased 
range  of  temperature  in  this  case  appears  to  give  a  possible 
advantage  of  9  per  cent.  Thus,  if  the  engine  working  as  a 
steam-engine  only  had  a  vacuum  of  27  inches  so  that  the  lower 
temperature  was  about  ii5°F.,  the  efficiency  of  Carnot's  cycle 
would  be 


-  115 


0.50, 


in  which  575  is  the  temperature  of  the  superheated  steam  supplied 
to  the  engine.     On  the  other  hand,  with  a   back-pressure  of 


BINARY    ENGINE  283 

about  35  pounds  in  the  sulphur-dioxide  cylinder  and  a  tempera- 
ture of  about  65°  F.,  the  efficiency  would  be 

T  -  T"  _  575  -  65 
T  575  +  460  " 

0.55     —    0X0 

and  — •*" ^—  =  o.oo. 

o-55 

The  results  of  the  tests  given  in  Table  XXVIII  are  somewhat 
difficult  to  use  as  a  basis  for  the  discussion  of  the  advantage  of 
the  binary  system  on  account  of  certain  discrepancies;  for  example, 
tests  No.  3  and  No.  7  have  substantially  the  same  total  power, 
steam-pressure,  superheating  and  vacuum,  and  nearly  the  same 
vapor- pressures  in  the  sulphur-dioxide  cylinder;  in  fact,  the 
advantage  appears  to  lie  slightly  in  favor  of  No.  7 ;  nevertheless, 
the  latter  test  is  charged  with  189  thermal  units  per  horse-power 
per  minute,  and  the  former  with  176,  giving  to  it  an  apparent 
advantage  of  about  7  per  cent.  A  comparison  of  steam  per 
horse-power  per  hour  gives  nearly  the  same  result.  A  com- 
parison of  tests  No.  2  and  No.  4  gives  even  a  more  striking 
discrepancy,  though  the  conditions  vary  more,  and  especially 
the  total  power  of  the  latter  is  much  greater. 

If  we  take  200  thermal  units  per  horse-power  per  hour  as  the 
best  result  from  a  steam-engine,  then  the  result  from  the  second 
test  appears  to  show  a  gain  of  16  per  cent,  while  the  seventh 
test  shows  a  gain  of  6  per  cent,  and  the  fourth  test  is  distinctly 
worse  than  the  standard  taken  for  the  steam-engine.  Under 
these  conditions  it  is  necessary  to  await  further  information. 

The  last  two  tests  made  with  the  engine  running  compound 
gave  results  that  are  a  trifle  better  than  those  for  the  compound 
engine  using  superheated  steam  but  as  it  probably  had  not 
the  most  favorable  proportions  the  comparison  is  hardly  fair. 

Test  No.  8  with  saturated  steam  gave  a  record  equivalent  to 
that  of  the  best  steam-engine,  which  is  distinctly  favorable  so 
far  as  it  goes,  as  the  steam-consumption  for  the  steam-engine  is 
large  even  making  allowance  for  so  poor  a  vacuum. 


284  ECONOMY    OF   STEAM-ENGINES 

Finally  it  appears  probable  that  the  best  results  for  the 
binary  engine  could  be  obtained  from  a  correctly  designed 
compound  engine,  using  superheated  steam;  or  nearly  as 
good  results  might  be  expected  for  saturated  steam  at  about 
175  pounds  gauge  pressure  with  steam-jackets.  Attention  has 
already  been  called  to  the  fact  that  steam-jackets  accomplish 
but  little  with  highly  superheated  steam,  and  appear  to  be 
unnecessary  and  illogical. 


CHAPTER   XIII. 

FRICTION    OF   ENGINES. 

THE  efficiency  and  economy  of  steam-engines  are  commonly 
based  on  the  indicated  horse-power,  because  that  power  is  a 
definite  quantity  that  may  be  readily  determined.  On  the 
other  hand,  it  is  usually  cjimcult  and  sometimes  impossible  to 
make  a  satisfactory  determination  of  the  power  actually  delivered 
by  the  engine.  A  common  way  of  determining  the  work  con- 
sumed by  friction  in  the  engine  itself  is  to  disconnect  the  driving- 
belt,  or  other  gear  for  transmitting  power  from  the  engine,  and 
to  place  a  friction- brake  on  the  main  shaft;  the  power  developed 
is  then  determined  by  aid  of  indicators,  and  the  power  delivered 
is  measured  by  the  brake,  the  difference  being  the  power  con- 
sumed by  friction.  Such  a  determination  for  a  large  engine 
involves' much  trouble  and  expense,  and  may  be  unsatisfactory, 
since  the  engine-friction  may  depend  largely  on  the  gear  for 
transmitting  power  from  the  engine,  especially  when  belts  or 
ropes  are  used  for  that  purpose. 

The  friction  of  a  pumping-engine  may  be  determined  from  a 
comparison  of  the  indicated  power  of  the  steam-cylinders  with 
the  indicated  work  of  the  pumps,  or,  better,  with  the  work  done 
in  lifting  water,  from  the  well  and  delivering  it  to  the  forcing- 
main.  But  the  friction  thus  determined  is  the  friction  of  both 
the  engine  and  the  pump.  Air-compressors  and  refrigerating 
machines  may  be  treated  in  the  same  way  to  determine  the  fric- 
tion of  both  engine  and  compressor.  Again,  the  combined 
friction  of  an  engine  and  a  directly  connected  electric  generator 
may  be  determined  by  comparing  the  indicated  power  of  the 
engine  with  the  electric  output  of  the  generator,  allowing  for 
electricity  consumed  or  wasted  in  the  generator  itself. 

The  friction  of  a  steam-engine  may  consume  from  5  to  15  per 

285 


286 


FRICTION    OF   ENGINES 


cent  of  the  indicated  horse-power,  depending  on  the  type  and 
condition  of  the  engine.  The  power  required  to  drive  the  air- 
pump  (when  connected  to  the  engine)  is  commonly  charged  to 
the  friction  of  the  engine.  It  is  usual  to  consider  that  seven  per 
cent  of  the  indicated  power  of  the  engine  is  expended  on  the 
air-pump.  Independent  air-pumps  which  can  be  driven  at  the 
best  speed  consume  much  less  power;  those  of  some  United 
States  naval  vessels  used  only  one  or  two  per  cent  of  the  power 
of  the  main  engines.  But  as  independent  air-pumps  are  usually 
direct-acting  steam-pumps,  much  of  the  apparent  advantage  just 
pointed  out  is  lost  on  account  of  the  excessive  steam-consump- 
tion of  such  pumps. 

Mechanical  Efficiency.  —  The  ratio  of  the  power  delivered  by 
an  engine  to  the  power  generated  in  the  cylinder  is  the  mechanical 
efficiency;  or  it  may  be  taken  as  the  ratio  of  the  brake  to  the 
indicated  power.  The  mechanical  efficiency  of  engines  varies 
from  0.85  to  0.95,  corresponding  to  the  per  cent  of  friction  given 
above. 

The  following  table  gives  the  mechanical  efficiencies  of  a 
number  of  engines,  determined  by  brake-tests,  or,  in  case  of  the 


TABLE  XXIX. 

MECHANICAL  EFFICIENCIES   OF   ENGINES. 


Kind  of  Engine. 

Horse-  Power. 

Efficiency. 

Simple  engines: 
Horizontal  portable 

24 

o  86 

Horizontal  portable  Hoadlev            

80 

O.QI 

High-speed,  straight-line  .        

c6 

O.f)6 

Corliss  condensing     

1  60 

0.81 

Corliss  rion  -condensing     

IOO 

0.86 

Compound  : 
Portable                                                                .    .    . 

78 

0.88 

Semi  -portable                                          

60 

0.88 

Horizontal                                        

CO 

O.QO 

288 

0.86 

Schmidt   superheated  steam 

I  IO 

O.Q2 

Leavitt  pumping-engine 

64.3 

O.Q2 

Triple-expansion  Leavitt  pumping-engine         .... 

;76 

O.QO 

INITIAL   FRICTION   AND    LOAD    FRICTION  287 

pumping-engines,  by  measuring  the  work  done  in  pumping 
water. 

Initial  Friction  and  Load  Friction.  —  A  part  of  the  friction  of 
an  engine,  such  as  the  friction  of  the  piston-rings  and  at  the 
stuffing-boxes  of  piston-rods  and  valve-rods,  may  be  expected 
to  remain  constant  for  all  powers.  The  friction  at  the  cross- 
head  guides  and  crank-pins  is  due  mainly  to  the  thrust  or  pull 
of  the  steam-pressure,  and  will  be  nearly  proportional  to  the  mean 
effective  pressure.  Friction  at  other  places,  such  as  the  main 
bearings,  will  be  due  in  part  to  weight  and  in  part  to  steam- 
pressure.  On  the  whole,  it  appears  probable  that  the  friction 
may  be  divided  into  two  parts,  of  which  one  is  independent  of 
the  load  on  the  engine,  and  the  other  is  proportional  to  the  load. 
The  first  may  be  called  the  initial  friction,  and  the  second,  the 
load  friction.  Progressive  brake-tests  at  increasing  loads  con- 
firm this  conclusion. 

Table  XXX  gives  the  results  of  tests  made  by  Walther-Meun- 
ier  and  Ludwig  *  to  determine  the  friction  of  a  horizontal-receiver 
compound  engine,  with  cranks  at  right  angles  and  with  a  fly- 
wheel, grooved  for  rope-driving,  between  the  cranks.  The 
piston-rod  of  each  piston  extended  through  the  cylinder-cover 
and  was  carried  by  a  cross-head  on  guides,  and  the  air-pump  was 
worked  from  the  high-pressure  piston-rod.  The  cylinders  each 
had  four  plain  slide-valves,  two  for  admission  and  two  for  exhaust; 
the  exhaust- valves  had  a  fixed  motion,  but  the  admission- valves 
were  moved  by  a  cam  so  that  the  cut-off  was  determined  by  the 
governor. 

The  main  dimensions  of  the  engine  were: 

Stroke 40.2  inches. 

Diameter:  small  piston 21.2  " 

large  piston 31.6  " 

piston-rods      3.2  " 

Diameter,  air-pump  pistons 14.2  " 

Stroke,  air-pump       18.8  " 

Diameter,  fly-wheel 24.1  " 

*  Bulletin  de  la  Soc.  Ind.  de  Mulhouse,  vol.   Ivii,  p.  140. 


288 


FRICTION    OF   ENGINES 


TABLE  XXX. 

FRICTION   OF  COMPOUND   ENGINE. 

WALTHER-MEUNIER    and    LUDWIG,    Bulletin    de    la    Soc.    Ind.    de    Mulhouse, 

vol.  Ivii,  p.  140. 


Horse-Powers  —  Chevaux  aux  Vapeur. 

Condition. 

Indicated. 

Effective. 

Absorbed 
by  Engine. 

vriction. 

Efficiency. 

I 

288.5 

249.0 

39-5 

°-I37 

0.863 

2 

. 

276.9 

238.9 

38.0 

0.138 

0.862 

3 

Compound 

265.6 

228.9 

36.7 

0.139 

0.861 

4 

condensing 

243-7 

208.8 

34-9 

0.144 

0.856 

5 

with 

222.7 

188.7 

34«o 

°-l53 

0.847 

6 

air-pump. 

201.5 

168.6 

32-9 

o.  164 

0.836 

7 

180.4 

148.5 

3*-9 

0.178 

0.822 

8 

158.1 

128.4 

29.7 

0.189 

0.811 

9 

136.  I 

108.3 

27.8 

o.  205 

o-795 

10 

I53-I 

128.4 

24.7 

o.  161 

0.839 

ii 

12 
13 
14 

High- 
pressure 
cylinder 

142.0 
130.9 
I2O.  I 
IO9.0 

118.3 
108.3 

98    2 

88.2 

23-7 

22.6 
21.9 
20.8 

o.  167 
0.173 
0.182 

0.  IOI 

0-833 
0.827 
0.818 
0.809 

3 

i? 

only. 
Condensing 
with 

97-5 
86.3 

75-7 

78.1 

68.1 
58.0 

19.4 

18.3 

17.7 

0.199 

0.212 
0.234 

0.801 
0.788 
0.766 

18 

air-pump. 

65-5 

48.0 

17-5 

0.267 

0-733 

19 

SS-2 

37-9 

17-3 

0-3I3 

0.687 

20 

145-9 

128.4 

J7-5 

0.  120 

0.880 

21 

*35-7 

118-3 

17.4 

o.  129 

0.871 

22 

High- 

125.2 

108.3 

16.9 

0-135 

0.865 

23 

pressure 

114.4 

98.2 

16.2 

o.  142 

0.858 

24 

cylinder 

103.9 

88.2 

15-7 

o.  152 

0.848 

25 

onlv. 

93  -° 

78.! 

14.9 

o.  1  60 

0.840 

26 

Non- 

82.0 

68.1 

13-9 

o.  170 

0.830 

27 

condensing, 

71.7 

58.0 

13-7 

0.191 

0.809 

28 

no  air-pump. 

61.6 

48.0 

13.6 

O.22I 

0.779 

29 

5i-3 

37-9 

13-4 

0.262 

0.738 

The  engine  during  the  experiments  made  58  revolutions  per 
minute.  The  air-pump  had  two  single-acting  vertical  pistons. 

Each  experiment  lasted  10  or  20  minutes,  during  which  the 
load  on  the  brake  was  maintained  constant,  and  indicator- 
diagrams  were  taken.  The  experiments  with  small  load  on  the 


INITIAL   FRICTION   AND    LOAD    FRICTION 


289 


brake  (numbers  9,  18,  19,  28,  and  29)  were  irregular  and  uncer- 
tain. 

The  first  nine  tests  were  made  with  the  engine  working  com- 
pound. Tests  10  to  19  were  made  with  the  high-pressure  cylin- 
der only  in  action  and  with  condensation,  the  low-pressure  con- 
necting-rod being  disconnected.  Tests  20  to  29  were  made  with 
the  high-pressure  cylinder  in  action,  without  condensation. 

The  results    of  these  tests  are  plotted  on  Fig.  60,  using  the 


-40 


-30 


ABSCISSAE,    EFFECTIVE  HORSEPOWER. 
OHDINA-TE8,    FRICTION    HORSEPOWER. 


100 


150 


FIG.  60. 

effective  horse-powers  for  abcissae  and  the  friction  horse-powers 
for  ordinates.  Omitting  tests  with  small  powers  (for  which  the 
brake  ran  unsteadily),  it  appears  that  each  series  of  tests  can  be 
represented  by  a  straight  line  which  crosses  the  axis  of  ordinates 
above  the  origin ;  thus  affording  a  confirmation  of  the  assumption 
that  an  engine  has  a-  constant  initial  friction,  and  a  load  friction 
which  is  proportional  to  the  load. 

Now  the  initial  friction  which  depends  on  the  size  and  con- 
struction of  the  engine  may  be  assumed  to  be  proportional  to  the 


FRICTION    OF   ENGINES 

normal  net  or  brake  horse-power,  Pn,  which  the  engine  is  designed 
to  deliver,  and  may  be  represented  by 

'P., 

where  a  is  a  constant  to  be  determined  from  a  diagram  like  Fig. 
60.  If  P  is  the  net  horse-power  delivered  by  the  engine  at  any 
time,  then  the  load  friction  corresponding  is 

bP, 

where  &  is  a  second  constant  to  be  determined  from  experiments. 
The  total  friction  of  the  engine  will  be 

F  =  aPn  +  bP, 
so  that  the  indicated  power  of  the  engine  will  be 

I.H.P.  =  P  +  aPn  +  bP  =  aPn  +  (i  +  b)P. 
The  mechanical  efficiency  corresponding  will  be 
I.H.P.  -  F  P 


em  = 


I.H.P.  I.H.P. 


The  compound  condensing  engine  for  which  tests  are  repre- 
sented by  Fig.  60  developed  290  I.H.P.  and  delivered  250  horse- 
power to  the  brake,  so  that  40  horse-power  were  consumed  in 
friction.  The  diagram  shows  also  that  the  initial  friction  was 
20  horse-power,  and  consequently  the  load  friction  was  20 
horse-power.  The  values  of  a  and  b  are  consequently 

a  =  20  -v-  250  =  0.07; 

b  =  (40  —  20)  -T-  250  =  0.07. 

The  indicated  horse-power  for  a  given  load  P  is 
I.H.P.  =  0.07  Pn  +  i.o'jP. 

Similar  equations  can  be  deduced  for  the  engine  with  steam 
supplied  to  the  small  cylinder  only;  but  as  the  engine  is  not  then 
in  normal  condition  they  are  not  very  useful. 

The  maximum  efficiency  of  this  engine  is 

250  -5-  290  =  0.86; 


INITIAL   FRICTION   AND    LOAD    FRICTION 


291 


but  at  half  load  (125  horse-power)  the  indicated  horse-power  Is 

I.H.P.  =  0.07  X  250  +  1.07  X  125  =  151, 
and  the  efficiency  is 

125  -^  151  =  0.83. 

TABLE  XXXI. 

FRICTION    OF   CORLISS    ENGINE    AT   CREUSOT. 
<     By  F.  DELAFOND,  Annales  des  Mines,  1884. 

Condensing  with  air-pump,  tests  1-33. 
Non-condensing  without  air-pump,  tests  34-46. 


Horse-Power  —  Cheval  h  Vapeur. 

Cut-off  Frac- 

Pressure at 

Revolutions 

tion  of 

Cut-off,  Kilos 

per  Minute. 

Stroke 

per  Sq.  Cm. 

Absorbed 

Indicated. 

Effective. 

by  Engine. 

I 

0.039 

0.64 

64.0 

27-8 

16.3 

ii   5 

2 

0.044 

2.40 

68.5 

60.0 

37-6 

22.4 

3 

0.044 

2.90 

65.0 

67.2 

45-2 

22  .O 

4 

0.065 

4-90 

64.0 

117.0 

88.7 

28.3 

5 

0.065 

6.  20 

61  .0 

138.5 

106.3 

32.2 

6 

0.065 

7.10 

64.0 

163.2 

129.  2 

34-0 

7 

0.065 

7.60 

64.0 

185.0 

144.6 

40.4 

8 

O.IOO 

0.16 

58.0 

21.0 

10.6 

10.4 

9 

o.  106 

1.55 

60.0 

6l.9 

42.3 

19.6 

10 

O.IOO 

2.82 

57-3 

82.7 

61  .0 

21.7 

ii 

0.090 

4.80 

58-3 

135-3 

106.7 

28.6 

12 

0.128 

4.82 

58.3 

154-5 

124.8 

29-7 

13 

0.142 

0.76 

62.0 

42.3 

28.4 

13-9 

14 

0.137 

0.71 

60.6 

44-3 

28.7 

15-6 

15 

0.132 

2.50 

54-0 

79-5 

59-8 

19.7 

16 

o.i47 

2.60 

61.6 

100.  0 

78.2 

21.8 

17 

0.155 

4-65 

60.0 

177.2 

32.2 

18 

0.167 

0.22 

61.0 

40.2 

27-9 

12.3 

19 

0.197 

2-55 

57-2 

no.  8 

83-3 

27.5 

20 

0.273 

O.4O 

62.3 

50.2 

33-8 

16.4 

21 

0.264 

1-57 

63-3 

89.1 

61.8 

27-3 

22 

0.240 

1.64 

62.0 

87.2 

63-1 

24.1 

23 

0.245 

3-25 

56.0 

i45-o 

116.0 

29.0 

24 

o.  260 

4.76 

58.0 

209.4 

178.0 

31.4 

25 

0.335 

0.25 

59-0 

47-2 

32.5 

14.7 

26 

0.339 

1.94 

58.3 

in.  7 

90.0 

21.7 

27 

0.338 

2.97 

61.0 

161.8 

133.0 

28.8 

28 

I 

0.47 

59-3 

81.3 

67.2 

14.1 

29 

I 

0-47 

61.0 

80.8 

67-9 

12.9 

30 

I 

i.  60 

61.6 

148.5 

128.4 

20.  I 

31 

I 

2.70 

61.5 

216.5 

191.0 

25-5 

32 

I 

2.70 

61.5 

215-5 

191.0 

24-5 

33 

0.50 

0.70 

6i-5 

15-8 

0.0 

15-8 

34 

0.120 

6.00 

60.0 

132.5 

107.5 

25.0 

35 
36 

0.106 

0.120 

7.00 
7-50 

62.0 

125.0 
172.0 

103.0 

148.0 

22.0 
24.0 

37 

0.150 

4-57 

55-0 

.     102.3 

86.5 

15-8 

38 

o.  262 

4-50 

59-0 

149.2 

132.3 

16.9 

39 

0.293 

4-55 

59-0 

171-8 

153-8 

18.0 

40 

0.371 

4-40 

60.0 

195-3 

177.2 

18.1 

4i 

0.348 

2.75 

58.0 

85.1 

12.0 

42 

0.348 

2-75 

58.5 

84.8 

71.1 

13-7 

43 

0.440 

3.48 

62.0 

151.0 

134-3 

I6.7 

44 

O.III 

3-30 

62.0 

12.8 

0.0 

12.8 

45 

0.50 

1.20 

62.0 

12.3 

0.0 

12.3 

46 

I 

O.50 

62.0 

10.45 

0.0 

10.45 

292 


FRICTION    OF   ENGINES 


Table  XXXI  gives  the  results  of  a  large  number  of  brake- 
tests  made  on  a  Corliss  engine  at  Creusot  by  M.  F.  Delafond, 
both  with  and  without  a  vacuum,  and  with  varying  steam- 
pressures  and  cut-off.  The  tests  with  a  vacuum  are  plotted 
on  Fig.  61,  and  those  without  a  vacuum  are  given  in  Fig.  62. 
In  both  figures  the  abscissae  are  the  indicated  horse-powers,  and 
the  ordinates  are  the  friction  horse-powers.  Most  of  the  tests 
are  represented  by  dots;  those  tests  which  were  made  with  the 
most  economical  cut-off  (one-sixth  for  the  engine  with  conden- 


x 

• 

>< 

^ 

• 

+  * 

^x 

• 

• 

•      ^^^ 

pr 

X 

j^^ 

Absci 

ssae,  in 

dicate( 

horse] 

)ovrer 

wx 

X: 

H 

c 
c 

> 

Ordin 

ates,  fr 

iction  ] 

vorsepo 

VfVT 

^ 

20           40           60           80          100        120         140         160         180         20 
FIG.  61. 

sation  and  one-third  without)  are  represented  by  crosses.  A 
few  tests  with  very  long  cut-off,  on  Fig.  61,  are  represented  by 
circles.  The  straight  lines  on  both  figures  are  drawn  to  represent 
the  tests  indicated  by  crosses.  In  general  the  points  representing 
tests  with  short  cut-off  and  high  steam-pressure  lie  above  the 
lines,  and  points  representing  tests  with  long  cut-off  and  low 
steam-pressure  lie  below  the  lines,  though  there  are  some  notable 
exceptions  to  this  rule.  The  circles  on  Fig.  61,  representing 
tests  with  cut-off  near  the  end  of  the  stroke,  show  much  less 


INITIAL   FRICTION    AND    LOAD    FRICTION 


293 


friction  than  the 'other  tests.  The  tests  on  this  engine  show 
clearly  that  both  initial  and  load  friction  are  affected  by  the 
cut-off  and  the  steam-pressure,  and  that  friction  tests  should 
be  made  at  the  cut-off  which  the  engine  is  expected  to  have  in 
service. 


Ordinates 


indie 
fricti 


n  hor.s 


ited  horse  pow 


power 


20 


40 


80          100         J20 
FIG.  6a. 


140 


160 


180        200 


The  initial  friction  was  eight  horse- power  both  with  and 
without  condensation.  But  p.  250  shows  that  the  engine 
with  condensation  gave  the  best  economy  when  it  indicated 
1 60  horse-power;  the  friction  was  then  30  horse-power,  so  that 
the  net  horse-power  was  130,  which  will  be  taken  for  the  normal 
horse-power  Pn.  Consequently 

a  =  8  -f-  130  =  0.06; 
b  =  (30  -  8)  -5-  130  =  0.17. 
.'.  I.H.P.  =  o.o62Pn  +  i.iyP. 

In  like  manner  Fig.  62  shows  the  best  economy  without 
condensation,  for  about  200  indicated  horse-power,  for  which 
the  friction  is  20  horse-power,  leaving  180  for  the  normal  power 
of  the  engine.  Consequently 

a  =  8  -5-  180  =  0.045; 
b  =  (20  —  8)  -4-  180  =  0.07. 
/.  I.H.P.  =  o.o45Pn  +  I.07P. 

This  engine  with  condensation  had  36  horse-power  expended 


294 


FRICTION    OF   ENGINES 


in  friction,  when  developing  200  horse-power;  without  conden- 
sation it  had  20;  consequently  the  air-pump  can  be  charged  with 

(36  —  20)  -v-  200  =  0.08 

of  the  indicated  power.     The  large  percentage  is  probably  due 
to  the  high  vacuum  maintained. 

Thurston's  Experiments.  —  As  a  result  of  a  large  number  of 
tests  on  non-condensing  engines,  made  under  his  direction  or 
with  his  advice,  Professor  R.  H.  Thurston  *  concluded  that, 
for  engines  of  that  type,  the  friction  is  independent  of  the 
load,  and  that  it  can,  in  practice,  be  determined  by  indicat- 
ing the  engine  without  a  load. 


TABLE   XXXII. 

FRICTION   OF   NON-CONDENSING   ENGINE. 

STRAIGHT-LINE   ENGINE,    8   INCHES    DIAMETER,    14    INCHES    STROKE. 


No.  of 
Diagram. 

Boiler- 
Pressure. 

Revolutions. 

Brake  H.P. 

I.  H.P. 

Frictional   H.P. 

I 

5° 

232 

4.06 

7.41 

3-35 

2 

65 

229 

4.98 

7.58 

2.6o 

3 

63 

230 

6.00 

IO.OO 

4.00 

4 

69 

230 

7.00 

10.27 

3-27 

5 

73 

230 

8.10 

"  75 

3.65 

6 

77 

230 

9.00 

12.  70 

3-70 

7 

75 

230 

10.00 

I4.O2 

4.02 

8 

80 

230 

TI.OO 

14.78 

3-78 

9 

80 

230 

I2.OO 

T5-I7 

3-17 

10 

35 

230 

13.00 

15.96 

2.96 

ii 

75 

230 

14.00 

16.86 

2.86 

12 

7° 

230 

15.00 

17.80 

2.80 

13 

72 

231 

2O.  IO 

22.07 

1.97 

14 

75 

230 

25.00 

28.31 

3-31 

IS 

60 

229        , 

29-55 

33  -°4 

3-40 

16 

58 

229 

34.86 

37.20 

2-34 

17 

70 

229 

39.85 

43  -°4 

3-i9 

18 

85 

230 

45.00 

47-79 

2    78 

iQ 

90 

230 

50.00 

52.60 

2.60 

20 

85 

230 

55.00 

57-54 

2-54 

Table  XXXII  gives  the  details  of  one  series  of  tests.  The 
friction  horse-power  is  small  in  all  the  tests,  and  the  variations 
are  small  and  irregular,  and  appear  to  depend  on  the  state  of 

*  Trans,  of  the  Am.  Soc.  of  Mech.  Engrs.,  vols.  viii,  ix,  and  x. 


DISTRIBUTION    OF   FRICTION 


295 


lubrication  and  other  minor  causes  rather  than  on  the  change 
of  load. 

Distribution  of  Friction.  —  As  a  consequence  of  his  conclusion 
in  the  preceding  section,  Professor  Thurston  decided  that  the 
friction  of  an  engine  may  be  found  by  driving  it  from  some 
external  source  of  power,  with  the  engine  in  substantially  the 
same  condition  as  when  running  as  usual,  but  without  steam  in  its 
cylinder,  and  by  measuring  the  power  required  to  drive  it  by 
aid  of  a  transmission  dynamometer.  Extending  the  principle, 
the  distribution  of  friction  among  the  several  members  of  the 
engine  may  be  found  by  disconnecting  the  several  members, 
one  after  another,  and  measuring  the  power  required  to  run  the 
remaining  members. 

The  summary  of  a  number  of  tests  of  this  sort,  made  by  Pro- 
fessor R.  C.  Carpenter  and  Mr.  G.  B.  Preston,  are  given  in 
Table  XXXIII.  Preliminary  tests  under  normal  conditions 
showed  that  the  friction  of  the  several  engines  was  practically 
the  same  at  all  loads  and  speeds. 

The  most  remarkable  feature  in  this  table  is  the  friction  of 
the  main  bearings,  which  in  all  cases  is  large,  both  relatively  and 
absolutely.  The  coefficient  of  friction  for  the  main  bearings, 
calculated  by  the  formula 

33,000   H.P. 
J  '  pen 

is  given  in  Table  XXXIV.  p  is  the  pressure  on  the  bearings  in 
pounds  for  the  engines  light,  and  plus  the  mean  pressure  on 
the  piston  for  the  engines  loaded;  c  is  the  circumference  of  the 
bearings  in  feet;  n  is  the  number  of  revolutions  per  minute, 
and  H.P.  is  the  horse-power  required  to  overcome  the  friction 
of  the  bearings. 

The  large  amount  of  work  absorbed  by  the  main  bearings 
and  the  large  coefficient  of  friction  appear  the  more  remarkable 
from  the  fact  that  the  coefficient  of  friction  for  car-axle  journals 
is  often  as  low  as  one-tenth  of  one  per  cent,  the  difference  being 
probably  due  to  the  difference  in  the  methods  of  lubrication. 


296 


FRICTION    OF    ENGINES 


TABLE   XXXIII. 

DISTRIBUTION   OF  FRICTION. 


Percent: 

iges  of  Total 

Friction. 

Parts  of  Engine. 

N 

xjj 

o  rt 
«>• 

i-  M 

C/3 

X-2 

*§ 

II  i 

m 
i5*. 

in  w 

7"  X  10"  Lansing 
Iron  Works  —  Trac- 
tion Locomotive 
Valve-Gear. 

12"  Xi8"  Lansing 
Iron  Works  — 
Automatic  Bal- 
anced Valve. 

1*1 

ls>§ 

^3* 

»Ss* 

a  "3 

x  2  S 

IVtain  Bearings 

47    O 

?C       A 

•ye    O 

41    6 

6j  •*¥ 

Piston  and  Rod  .    . 

•22    Q 

2C    o 

21     O 

Crank  Pin    

6  8 

c    i 

I  "?    O 

49.1 

21.  8 

Cross  Head  and  Wrist  Pin 

5-4 

4.1 

Valve  and  Rod    

2  .  C 

26.4 

Eccentric  Strap 

57 

4O 

22.0 

9-3 

21.0 

Link  and  Eccentric        .    . 
Air-  Pump     

... 

... 

9.0 

•    • 

I  •?  O 

Total     

IOO.O 

IOO.O 

IOO.O 

IOO.O 

IOO  O 

TABLE   XXXIV. 

COEFFICIENT  OF  FRICTION    FOR  THE   MAIN   BEARINGS   OF 
STEAM-ENGINES. 


°~ 

M 

0    M 

H-  )   U 

•s-I 

V 

o"|  f 

"3 

(A    "— 

«  8 

'-•>  § 

Engine. 

9  3 
*°  0 

§1 

°« 

lo*i 

lfl-1 

|-ss 

Si 

£.2 

1- 

ll'J 

|l' 

1|I 

**-2> 

r  '  S 

^   rt 

rt  g 

O'u 

O  '^* 

•?  a 

Q 

fe 

ta 

6"  X  1  2"  Straight-line     .    .    . 

0.85 

1500 

3 

.  10 

.06 

230 

*i2"X  1  8"  Automatic  (L.  I.  W.  ) 

3-7° 

2600 

.19 

•°5 

190 

7"X  10"  Traction  (L.  I.  W.)  . 

0.68 

500 

2| 

•31 

.08 

200 

2i"X  20"  Condensing  (L.  I.  W.) 

3.30 

4000 

5i 

.09 

.04 

206 

*  The  i2/fXi&ff  automatic  engine  was  new,  and  gave,  throughout,  an  exces- 
sive amount  of  friction  as  compared  with  the  older  engines  of  the  same  class  and 
make. 


DISTRIBUTION    OF   FRICTION  297 

The  second  and  obvious  conclusion  from  Table  XXXIII  is 
that  the  valve  should  be  balanced,  and  that  nine-tenths  of  the 
friction  of  an  unbalanced  slide-valve  is  unnecessary  waste. 

The  friction  of  the  piston  and  piston-rod  is  always  considerable, 
but  it  varies  much  with  the  type  of  the  engine,  and  with  differ- 
ences in  handling.  It  is  quite  possible  to  change  the  effective 
power  of  an  engine  by  screwing  up  the  piston-rod  stuffing-box 
too  tightly.  The  packing  of  both  piston  and  rod  should  be  no 
tighter  than  is  necessary  to  prevent  perceptible  leakage,  and  is 
more  likely  to  be  too  tight  than  too  loose. 


CHAPTER  XIV. 

INTERNAL-COMBUSTION    ENGINES. 

RECENT  advances  in  the  generation  of  power  from  heat  have 
been  found  in  the  development  of  internal-combustion  engines 
and  of  steam-turbines;  the  latter  will  be  treated  in  Chapter  XIX. 
When  first  introduced  the  only  convenient  fuel  for  internal-com- 
bustion or  gas-engines  was  illuminating-gas,  which  limited  their 
use  to  small  sizes,  for  which  convenience  and  small  cost  of  attend- 
ance offset  the  cost  of  fuel.  Twenty  years  ago  an  engine  of  fifty 
horse-power  was  a  large  though  not  an  unusual  size.  At  that 
time  Mr.  Dowson  had  succeeded  in  generating  gas  from  anthra- 
cite coal  and  from  coke  in  his  producer.  Ten  years  ago  engines 
of  400  horse-power  were  built  to  use  Dowson  producer  gas,  but 
as  they  had  four  cylinders  the  horse-power  per  cylinder  was  only 
twice  that  of  single-cylinder  engines  of  a  decade  earlier;  the 
fuel  used  in  the  producer  was  a  cheap  grade  of  anthracite.  At 
the  present  time,  gas-engines  are  in  use  which  develop  as  much 
as  1500  horse-power  per  cylinder;  these  engines  are  of  the  two- 
cycle  double-acting  type.  The  application  of  gas-engines  to 
marine  propulsion  may  now  be  considered  to  be  fairly  under 
way,  though  as  yet  the  vessels  so  propelled  have  been  of  small 
displacement;  certain  British  firms  of  shipbuilders  have  plans 
matured  for  the  application  of  such  engines  to  the  propulsion 
of  large  ships. 

Hot-air  Engines.  —  Though  the  attempt  to  develop  hot-air 
engines  on  a  large  scale  appears  to  be  definitely  abandoned,  and 
though  the  interest  of  this  type  of  engine  is  mainly  historical  a 
brief  discussion  of  them  has  some  advantage,  for,  after  all,  the 
internal-combustion  engine  is  a  hot-air  engine  in  which  heat  is 
applied  by  burning  fuel  in  the  cylinder. 

In  the  discussion  of  the  second  law  of  thermodynamics  (see 

298 


STIRLING'S    ENGINE 


299 


page  39)  it  was  pointed  out  that  to  obtain  the  maximum  effi- 
ciency all  the  heat  must  be  added  at  the  highest  practicable  tem- 
perature, and  the  heat  rejected  must  be  given  up  at  the  lowest 
temperature.  The  hot-air  engine  is  the  only  attempt  to  follow 
the  example  of  Carnot's  engine  by  supplying  heat  to  and  with- 
drawing heat  from  a  constant  mass  of  working  substance  (air). 
An  attempt  to  obtain  the  diagram  of  Carnot's  cycle  from  such 
an  engine  would  involve  the  difficulty  that  the  acute  angle  at 
which  the  isothermal  and  adiabatic  lines  for  air  cross,  gives  a 
very  long  and  attenuated  diagram  that  could  be  obtained  only 
by  an  excessively  large  working  cylinder,  with  so  much  friction 
that  the  effective  power  delivered  by  the  engine  would  be  insigni- 
ficant. This  is  illustrated  by  Problem  20,  page  75.  To  obviate 
this  difficulty  Stirling  invented  the  economizer  or  regenerator 
which  replaced  the  adiabatic  lines  by  vertical  lines  of  constant 
volume,  and  thus  obtained  a  practical  machine.  His  type  of 
engine  is  still  employed,  but  only  for  very  small  pumping-engines 
which  are  used  for  domestic  purposes,  as  they  are  free  from  dan- 
ger and  require  little  attention. 

Stirling's  Engine. — This  engine  was  invented  in  1816,  and 
was  used  with  good  economy  for  a  few  years,  and  then  rejected 
because  the  heaters,  which  took  the  place  of  the  boiler  of  a  steam- 
engine,  burned  out  rapidly;  the  small  engines  now  in  use  have 
little  trouble  on  this  account.  It  is  described 
and  its  performance  given  in  detail  by  Rankine 
in  his  "Steam- Engine."  An  ideal  sketch  is 
given  by  Fig.  63.  E  is  a  displacer  piston  filled 
with  non-conducting  material,  and  working 
freely  in  an  inner  cylinder.  Between  this 
cylinder  and  an  outer  one  from  A  to  C  is 
placed  a  regenerator  made  of  plates  of  metal, 


wire  screens,   or  other  material,  so  arranged 

that  it  will    readily  take   heat  from  or  yield  FlG<  6s> 

heat  to  air  passing  through  it.     At  the  lower 

end  both  cylinders  have  a  hemispherical  head ;  that  of  the  outer 

cylinder  is  exposed  to  the  fire  of  the  furnace,  and  that  of  the 


300 


INTERNAL-COMBUSTION    ENGINES 


inner  is  pierced  with  holes  through  which  the  air  streams  when 
displaced  by  the  plunger.  At  the  upper  end  there  is  a  coil  of 
pipe  through  which  cold  water  flows.  The  working  cylinder  H 
has  free  communication  with  the  upper  end  of  the  displacer 
cylinder,  and  consequently  it  can  be  oiled  and  the  piston  may 
be  packed  in  the  usual  manner,  since  only  cool  air  enters  it. 

In  the  actual  engine  the  cylinder  H  is  double-acting,  and 
there  are  two  displacer  cylinders,  one  for  each  end  of  the  working 
cylinder. 

If  we  neglect  the  action  of  the  air  in  the  clearance  of  the 
cylinder  H  and  the  communicating  pipe,  we  have  the  following 
ideal  cycle.  Suppose  the  working  piston  to  be  at  the  beginning 
of  the  forward  stroke,  and  the  displacer  piston  at  the  bottom  of 
its  cylinder,  so  that  we  may  assume  that  the  air  is  all  in  the  upper 
part  of  that  cylinder  or  in  the  refrigerator,  and  at  the  lowest  tem- 
perature T2)  the  condition  of  one  pound  of  air  being  represented 
by  the  point  D  of  Fig.  64.  The  displacer  piston  is  then  moved 
quickly  by  a  cam  to  the  upper  end  of  the 
stroke;  while  the  working  piston  moves  so 
little  that  it  may  be  considered  to  be  at  rest. 
The  air  is  thus  all  driven  from  the  upper  end 
of  the  displacer  cylinder  through  the  regene- 
rator, from  which  it  takes  up  heat  abandoned 


FIG.  64.  during  the   preceding   return    stroke,  thereby 

acquiring  the  temperature  Tv  and  enters  the 
lower  end  of  that  cylinder.  During  this  process  the  line  AD  of 
constant  volume  is  described  on  Fig.  64.  When  this  process  is 
complete,  the  working  cylinder  makes  the  forward  stroke,  and 
the  air  expands  at  constant  temperature,  this  part  of  the  cycle 
being  represented  by  the  isothermal  AB  of  Fig.  64.  At  the  end 
of  the  forward  stroke  the  displacer  piston  is  quickly  moved 
down,  thereby  driving  the  air  through  the  regenerator,  during 
which  process  heat  is  given  up  by  the  air,  into  the  upper  part 
of  the  displacer  cylinder;  this  is  accompanied  by  a  cooling  at 
constant  volume,  'represented  by  the  line  EC.  The  working 
piston  then  makes  the  return  stroke,  compressing  the  air  at  con- 


STIRLING'S    ENGINE 


301 


stant  temperature,  as  represented  by  the  isothermal  line  CD,  and 
completing  the  cycle. 

To  construct  the  diagram  drawn  by  an  indicator,  we  may 
assume  that  in  the  clearance  of  the  cylinder  H,  the  communi- 
cating pipe,  and  refrigerator  there  is  a  volume  of  air  which  flows 
back  and  forth  and  changes  pressure,  but  remains  at  the  tempera- 
ture T2.  If  we  choose,  we  may  also  make  allowance  for  a  simi- 
lar volume  which  remains  in  the  waste  spaces  at  the  lower  end 
of  the  displacer  cylinder,  at  a  constant  temperature  Tr 

In  Fig.  65,  let  ABCD  represent  the  cycle  of  operations,  with- 
out any  allowance  for  clearance  or  waste  spaces;  the  minimum 
volume  will  be  that  displaced  by  the  displacer  piston,  while  the 
maximum  volume  is  larger  by  the  volume  displaced  by  the  work- 
ing piston.  Let  the  point  E  represent  the  maximum  pressure, 
the  same  as  that  at  A ;  and  the  united  volumes  of  the  clearance 
at  one  end  of  the  working  cylinder,  of  the  communicating  pipe, 


FIG.  65. 


of  the  clearance  at  the  top  and  bottom  of  the  displacer  cylinder, 
and  the  volume  in  the  refrigerator  and  regenerator.  Each  part 
of  this  combined  volume  will  have  a  constant  temperature,  so 
that  the  volume  at  different  pressures  will  be  represented  by  the 
hyperbola  EF.  To  find  the  actual  diagram  A'B'C'D',  draw 
any  horizontal  line,  as  sy,  cutting  the  true  diagram  at  u  and  X, 
and  the  hyperbola  EF  at  /;  make  uv  and  xy  equal  to  st\  then 
v  and  y  are  points  of  the. actual  diagram.  The  indicator  will 
draw  an  oval  similar  to  A'B'C'D'  with  the  corners  rounded. 

The  diagram  in  Fig.  66  was  reduced  from  an  indicator-dia- 
gram  from    a    hot-air    engine    made    on    the    same    principle 


302 


INTERNAL-COMBUSTION    ENGINES 


as  Stirling's  hot-air  engine.  To  avoid  destruction  of  the  lubri- 
cant in  the  working  cylinder  Stirling  found  it  advisable  to  con- 
nect only  the  cool  end  of  the 
displacer  cylinder  with  the  working 
cylinder,  and  had  two  displacer 
cylinders  for  one  working  cylinder. 

It   has   been   found    that    a    good 

FIG.  66.  mineral  oil  can  be  used  to  lubricate 

the  displacer  piston,  and  that  the 

hot  end  also  of  the  displacer  cylinder  can  be  advantageously 
connected  with  the  working  cylinders,  of  which  there  are  two. 
Thus  each  working  cylinder  is  connected  with  the  hot  end  of 
one  displacer  cylinder  and  with  the  cool  end  of  the  other 
displacer  cylinder. 

The  distortion  of  the  diagram  Fig.  66  is  due  in  part  to  the 
large  clearance  and  waste  space,  and  partly  to  the  fact  that 
the  displacer  pistons  are  moved  by  a  crank  at  about  70  degrees 
with  the  working  crank. 

A  test  on  the  engine  mentioned  by  Messrs.  Underhill  and 
Johnson  *  showed  a  consumption  of  1.66  of  a  pound  of  anthracite 
coal  per  horse-power  per  hour;  but  the  friction  of  the  engine  is 
large,  so  that  the  consumption  per  brake  horse-power  is  2.37 
pounds.  This  engine,  like  the  original  Stirling  engine,  appears 
to  have  given  much  difficulty  from 
the  burning  of  the  heaters.  The 
difficulty  is  likely  to  be  more  serious 
with  large  than  with  small  engines, 
as  the  volume  of  the  displacer  cylin- 
ders increases  more  rapidly  than  the 
heating  surface. 

The  action  of  the  regenerator  may 
be  best  explained  by  redrawing  the 
diagram  Fig.  64  on  the  temperature- 
entropy  plane  as  shown  in  Fig.  67, 
where  AB  and  CD  are  constant  temperature  lines  representing 

*  Thesis,  M.  I.  T.  1889. 


T+AT 

f 

J 

C^ 

T    y 

Yy 

0 

vy 

D 

X 

d  wxa            c  yz  b 
FIG.  67. 

STIRLING'S    ENGINE  303 

isothermal  expansion,  and  DA  and  BC  take  the  place  of 
the  constant  volume  lines  on  Fig.  64.  To  show  that  these 
lines  are  properly  drawn,  we  may  consider  the  equation 


dt   ,  .dv 

-+(Cp-cv)- 


which    was    deduced    on    page    67.     For    the    lines    DA     and 
BC  the  volumes  are  constant,  so  that  the  equation  reduces  to 

,:  dt 

d<f>  =  cv  — ; 

or  transposing, 

dt        T  . 

j  ,  —       5 
a<p       cv 

but  this  last  expression  represents  the  tangent  of  the  angle  between 
the  axis  O®  and  the  tangent  to  the  curve.  This  angle  increases 
(but  with  a  diminishing  ratio)  with  the  temperature,  and  as  cv 
is  constant  for  a  gas,  the  angle  depends  only  on  the  temperature 
T,  so  that  the  curve  BC  is  identical  in  form  with  the  curve  AD, 
and  is  merely  set  off  further  to  the  right;  in  consequence,  parts 
like  WX  and  ZY  between  a  pair  of  constant  temperature  lines 
are  identical  except  in  their  positions  with  regard  to  the  axis  OT. 
Suppose  now  that  the  material  of  the  regenerator  has  the 
temperature  Tl  at  the  lower  end  and  T2  at  the  upper  end,  and 
that  the  temperature  varies  regularly  from  bottom  to  top.  Sup- 
pose further  that  the  air  when  giving  heat  to  the  regenerator 
(or  receiving  heat  from  it)  differs  from  it  by  only  an  inappreci- 
able amount.  Then  the  diagram  of  Fig.  67  will  represent  this 
ideal  action  correctly,  and  it  is  easy  to  show  that  its  efficiency 
is  the  same  as  that  of  Carnot's  cycle  ABC'D'.  For  the 
amount  of  heat  acquired  by  the  regenerator  during  the  opera- 
tion represented  by  BC,  corresponding  to  the  down  stroke  of 
the  displacer  piston,  is  measured  by  the  area  bBCc;  and  the 
heat  yielded  during  the  up  stroke  DA,  is  represented  by 
the  area  dDAa;  and  these  two  areas  are  manifestly  equal. 


304  INTERNAL-COMBUSTION    ENGINES 

Moreover,  the  small  amount  of  heat  gained  during  the  operation 
ZY  at  the  temperature  T  is  exactly  counterbalanced  by  the 
heat  yielded  during  the  operation  XW  at  the  same  temperature, 
so  that  there  is  no  loss  of  efficiency;  the  small  amounts  of  heat 
mentioned  are  represented  by  the  equal  areas  zZ  Yy  and  wWXx. 

It  can  be  shown  that  one  of  the  curves  like  DA  may  be  drawn 
at  random,  provided  that  the  other  curve  like  BC  is  made  iden- 
tical and  set  off  further  to  the  right;  but  the  matter  is  not  of 
importance  enough  to  warrant  its  discussion. 

In  practice  a  regenerator  must  be  at  an  appreciably  lower 
temperature  than  the  air  from  which  it  receives  heat,  and  at  a 
higher  temperature  than  that  to  which  it  yields  heat,  as  the  flow 
of  air  is  rapid.  The  loss  of  heat  stored  and  restored  per  cycle 
of  the  original  Stirling  engine  was  estimated  at  five  per  cent  to 
ten  per  cent.  It  may  be  proper  before  passing  from  the  subject 
state  that  regenerators  are  not  applicable  to  gas-engines  in  use 
at  the  present  day. 

Gas-Engines.  —  The  chief  difficulty  with  hot-air  engines  is 
to  transmit  heat  to  and  from  the  working  substance.  In  gas- 
engines  this  difficulty  is  removed  by  mixing  the  fuel  with  the 
air  (so  that  heat  is  developed  in  the  working  substance  itself), 
and  by  rejecting  the  hot  gases  after  they  have  done  their  work. 
The  fuel  may  be  illuminating-gas,  fuel-gas,  or  vapor  of  a  volatile 
liquid  like  gasoline.  It  will  be  shown  that  the  specific  volume 
and  the  specific  heat  of  the  mixture  of  air  and  gas,  both  before 
and  after  the  heat  is  developed  by  combustion,  are  not  very 
different  from  the  same  properties  of  air.  The  general  theory 
of  gas-engines  may  therefore  be  developed  on  the  assumption 
that  the  working  substance  is  air,  which  is  heated  and  cooled  in 
such  a  manner  as  to  produce  the  ideal  cycles  to  be  discussed, 
as  is  done  by  Clerk.* 

Experience  has  shown  that  in  order  to  work  efficiently,  the 
mixture  of  gas  and  air  supplied  to  a  gas-engine  must  be  com- 
pressed to  a  considerable  pressure  before  it  is  ignited.  This  may 
be  done  either  by  a  separate  compressor  or  in  the  cylinder  of  the 

*  The  Gas  and  Oil  Engine  :    Dugald  Clerk. 


GAS-ENGINE    WITH    SEPARATE    COMPRESSOR  305 


-D 


engine  itself;  the  second  type  of  engines,  of  which  the  Otto 
engine  is  an  example,  is  the  only  successful  type  at  the  present 
time;  the  other  type  has  some  advantages  which  may  lead  to  its 
development. 

Gas-Engine  with  Separate  Compressor.  —  This  engine  has 
a  compressor,  a  reservoir,  and  a  working  cylinder.  When  run 
as  a  gas-engine  a  mixture  of  gas  and  air  is  drawn  into  a  pump  or 
compressor,  compressed  to  several  atmospheres,  and  forced  into 
a  receiver.  On  the  way  from  the  receiver  to  the  working  cylinder 
the  mixture  is  ignited  and  burned  so  that  the  temperature  and 
volume  are  much  increased.  After  expansion  in  the  working 
cylinder  the  spent  gases  are  exhausted  at  atmospheric  pressure. 

The  ideal  diagram  is  represented  by  Fig.  68.     ED  represents 
the  supply  of  the  combustible  mixture  to  the 
compressor,  DA  is  the  adiabatic  compres- 
sion,  and   AF  represents  the  forcing  into 
the    receiver.     FB    represents    the    supply 
of   burning   gas   to   the   working   cylinder, 
BC  represents  the   expansion,  and  CE  the 
exhaust.     In   practice   this   type   of   engine 
always  has  a  release,  represented  by  GH,  before  the  expansion 
has  reduced  the  pressure  of  the  working  substance  to  that  of  the 
atmosphere. 

This  type  of  engine  has  been  used  as  an  oil-engine  by  supplying 
the  fuel  in  the  form  of  a  film  of  oil  to  the  air  after  it  has  been 
compressed.  In  such  case  the  compressor  draws  in  air  only, 
and  there  is  not  an  explosive  mixture  in  the  receiver.  The 
Brayton  engine  when  run  in  this  way  could  burn  crude  petroleum, 
or,  after  it  was  started,  could  burn  refined  kerosene.  Its  chief 
defect  appears  to  have  been  incomplete  combustion  and  conse- 
quent fouling  of  the  cylinder  with  carbon. 

The  effective  cycle  may  be  considered  to  be  represented  by 
the  diagram  A  BCD  (Fig.  68),  and  may  be  assumed  to  be  pro- 
duced in  one  cylinder  by  heating  the  air  from  A  to  B,  by  cooling 
it  from  C  to  Z>,  and  by  the  adiabatic  expansion  and  compression 
from  B  to  C  and  from  D  to  A  .  If  Ta  and  Tb  are  the  absolute 


306  INTERNAL-COMBUSTION    ENGINES 

temperatures  corresponding  to  the  points  A  and  J5,  then  the 
heat  added  from  A  to  B  is 

cp  (T,  -  T.), 
and  the  heat  withdrawn  from  C  to  D  is 

cr(T,-  Td), 
so  that  the  efficiency  of  the  ideal  cycle  is 

cp  (Tb  -  T.)  -  cp  (T.  -  Td)  T.  -  Td 

cp  (Tt  -  T.)  Tt-T."  (  77) 

But  since  the  expansion  and  compression  are  adiabatic, 


Tb  ~    p         '  Ta        p 
but  pe  =  pd  and  pb  =  pa,  therefore 


T.  Td  Tc-  Td  Tf1 
—  =  —  and--  --  r"^"^ 
-fb  Ta  lb  —  la  la  \p 

so  that  the  equation  for  efficiency  becomes 


This  discussion  of  ideal  efficiency  is  due  to  Dugald  Clerk,*  and 
has  the  advantage  of  replacing  an  exceedingly  complex  operation 
by  a  simple  ideal  operation  which  has  approximately  the  same 
efficiency.  How  far  the  ideal  cycle  can  be  used  to  determine 
the  probable  advantages  of  certain  conditions  depends  on  the 
degree  of  approximation,  —  a  matter  which  will  be  referred 
to  later.  It  must  be  admitted  that  the  divergence  of  the 
actual  from  the  real  cycle  is  much  greater  than  the  divergence 
of  the  steam-engine  cycle  from  that  of  a  non-conducting 
cylinder. 

For  example,  with  the  pressure  in  the  reservoir  at  90  pounds 

*  The  Gas  Engine,  1886;  The  Gas  and  Oil  Engine,  1896. 


GAS-ENGINE    WITH    SEPARATE    COMPRESSOR  307 

above  the  atmosphere  the  efficiency  is 


1.405 


I    —      —* I  ==   0.43. 

Vi4-7  +  go/ 

When  the  cycle  is  incomplete  the  expression  for  the  efficiency 
is  not  so  simple,  for  it  is  necessary  to  assume  cooling  at  constant 
volume  from  G  to  H  (Fig.  68),  and  cooling  at  constant  pressure 
from  H  to  D\  so  that  the  heat  rejected  is 

cv  (Tg  -  Th)  +  cp  (Th  -  Td), 
and  the  efficiency  becomes 

r  (T.  -  T,)  +  (Th  -  Td~) 


-  b   —      -  a 

For  example,  let  it  be  assumed  that  the  pressure  at  A  is  90 
pounds  above  the  atmosphere,  that  the  temperature  at  B  is  2500° 
F.,  and  that  the  volume  at  G  is  three  times  the  volume  at  B. 

First,  the  temperature  at  A  is 

*  —  *  0.40S. 


provided  that  the  temperature  of  the  atmosphere  is  60°  F. 
The  temperature  at  G  is 

°s 


and  the  pressure  at  G  is 

Cvb\*  /iV  -4°5 

~)  --=  (i4.7  +9°)(-J       =.22.4  pounds, 


so  that  the  temperature  at  H  is 

r.-rf£-,  897x^-1.47, 

and  finally  the  efficiency  is 

(1897  -  1247)  +  1247  -  520 


i  --  •  —  -  -  -  —  --  ^  0.42 
2960  —  917 


308  INTERNAL-COMBUSTION    ENGINES 

Gas-Engines  with  Compression  in  the  Cylinder.  —  All  success- 
ful gas-engines  of  the  present  day  compress  the  explosive  mixture 
in  the  working  cylinder.  Very  commonly  they  take  gas  at  one 
end  of  the  cylinder  only,  and  require  four  strokes  to  complete 
the  cycle,  so  that  there  is  one  explosion  for  two  revolutions  when 
working  at  full  power.  Such  engines  are  commonly  known  as 
four-cycle  engines.  Some  engines  have  the  exhaust  and  filling 
of  the  cylinder  accomplished  in  some  other  way,  and  are  known 
as  two-cycle  engines;  they  have  an  explosion  for  every  revolu- 
tion when  single-acting.  Both  four-cycle  and  two-cycle  engines 
have  been  made  double-acting  in  large  sizes.  The  first  forward 
stroke  of  the  piston  from  the  head  of  the  cylinder  draws  in  the 
mixture  of  gas  and  air,  which  is  compressed  on  the  return  stroke ; 
at  the  completion  of  this  return  stroke  the  mixture  is  ignited  and 
the  pressure  rises  very  rapidly;  the  next  forward  stroke  is  the 
working  stroke,  which  is  succeeded  by  an  exhaust-stroke  to 
expel  the  spent  gases.  In  almost  all  engines  these  four  strokes 
are  of  equal  length,  for  the  advantage  of  making  them  of  unequal 
length,  as  required  for  the  best  ideal  cycle,  is  more  than  coun- 
terbalanced by  the  mechanical  difficulty  of  producing  unequal 
strokes. 

The   most  perfect  ideal  cycle,  represented  by  Fig.   69,   has 

four  strokes  of  unequal  length  so 
arranged  that  the  piston  starts  from 
the  head  of  the  cylinder  when  gas 
is  drawn  in,  and  the  pressure  in  the 
cylinder  is  reduced  to  that  of  the 
atmosphere  before  the  exhaust  stroke , 
Thus  there  is  the  filling  stroke, 
represented  by  EC;  the  compression 
stroke,  represented  by  CD\  the 
working  stroke,  represented  by  AE\ 


no.  69.  and  the  exhaust   stroke,    represented 

by  BE. 

The  effective  cycle  is  ABCD,  which  may  be  considered  to 
be  performed  by  adding  heat  at  constant  volume  from  D  to  A, 


GAS-ENGINES    WITH    COMPRESSION    IN    THE    CYLINDER   309 

and  withdrawing  heat  at  constant  pressure  from  B  to  C,  together 
with  the  adiabatic  expansion  and  compression  AB  and  CD. 
The  heat  added  under  this  assumption  is 

cv(Ta  -  Td\ 
and  the  heat  rejected  is 

c,  (Tt  -  Te), 

so  that  the  efficiency  is 

cv  (Ta  -  Td)  -  cv  (Tb-  Tf)                  Tb-Te  . 

«   = —7^ T}  —  =  i  -  * —  .        (180) 

Cv  (J-  a   ~    J-  d)  J-  a  —  *  d 

If  the  temperature  at  A  and  the  pressure  at  D  are  assumed, 
then  it  is  necessary  to  make  preliminary  calculations  of  the 
temperatures  at  D  and  at  B  before  using  equation  (180).  Thus, 
adiabatic  compression  from  C  to  D  gives  for  the  temperature 
at  D 


r«  - r-  (59     (iSi) 

in  like  manner  adiabatic  expansion  from  A  to  B  gives 


in  which  the  value  of  pa  may  be  calculated  by  the  equation 

Pa    =Pd    jr (183) 

j-d 

since  the  pressure  rises  with  the  temperature  at  constant  volume 
from  D  to  A. 

For  example,  if  the  pressure  at  the  end  of  compression  is 
90  pounds  above  the  atmosphere,  and  the  temperature  at  the 
end  of  the  explosion  is  2500°  F.,  then 


14.7 


310 


INTERNAI^COMBUSTION    ENGINES 


provided  that  the  temperature  of  the  atmosphere  is  60°  F. 

460 


pa  =  104.7 


338  pounds; 


T6=  (2500+460)  (2±^ 


Q-405 
i.405 


e  =  i  -  1.405 


1199  —  520 
2960  —  917 


FIG.  70. 


If  the  expansion  is  not  carried  to  the 
atmospheric  pressure,  then  the  diagram 
shows  a  release  at  the  end  of  the  stroke, 
as  in  Fig.  70,  and  the  cycle  must  be 
considered  to  be  formed  by  adding 
heat  as  before  at  constant  volume,  but 
by  withdrawing  heat  at  constant  volume 
to  cause  a  loss  of  pressure  from  B  to 
G,  and  by  withdrawing  heat  at  con- 
stant pressure,  during  the  process 


represented  by  GC.     The  heat  rejected  becomes,  therefore, 

c.  (Tb  -  TV)  +  cp(Tg  -  Te), 
and  the  efficiency  is 

c.  (Ta  -  Td)  -  cv  (Tb  -  TV)  -  cv  (Ta  -  TV) 
cv  (Ta  -  Td) 


e  = 


i  — 


TV  -  TV  +  *  (Tg  -  Tc) 


(184) 


Assuming,  as  before,  the  pressure  at  D  and  the  temperature 
at  A,  it  becomes  necessary  to  find  the  temperatures  at  B  and  at 
G  as  well  as  the  temperature  at  D]  this  last  may  of  course  be 
found  by  equation  (181).  If  the  pressure  at  B  is  assumed  also, 
then  equations  (182)  and  (183)  may  be  used  as  before  to  find 
Tb\  and  Tg  may  be  found  by  the  equation 


T   = 

• 


A 


GAS-ENGINES    WITH    COMPRESSION    IN    THE   CYLINDER   311 


For  example,  let  it  be  assumed  that  the  expansion  ceases 
when  the  pressure  becomes  20  pounds  above  the  atmosphere, 
'the  other  conditions  being  as  in  the  previous  example.  Then 


0.405 


,536 


^  = 


and 


i  — 


1536  —  650  +  1-405  (650  —  520) 
2960  —  917 


=  0.48. 


Though  not  essential  to  the  solution  of  the  example,  it  is 
interesting  to  know  that  the  volume  at  C  is 


go  + 


14.7 


=  4 


times  the  volume  at  D,  and  that  the  volume  at  B  is 


V34- 


=  5  + 


times  the  volume  at  A. 

When,  as  in  common  practice,  the 
four  strokes  of  the  piston  .are  of  equal 
length,  the  diagram  takes  the  form  shown 
by  Fig.  71;  the  effective  cycle  may  be 
considered  to  be  equivalent  to  heating  at 
constant  volume  from  D  to  A  and  cooling 
at  constant  volume  from  B  to  C,  together 
with  adiabatic  expansion  and  compression 
from  A  to  B  and  from  C  to  D 


FIG.  ft. 


312  INTERNAL-COMBUSTION    ENGINES 

The  heat  applied  is 

r    (T      -  T  \ 
cv  \*  a  -L  d)j 

and  the  heat  rejected  is 

c,  (T,  -  Te), 
so  that  the  efficiency  is 

.  =  *  (T.  -*£  ~  *n  ~  r.)  =  T_  £=£.  (I86) 

Since  the  expansion  and  compression  are  adiabatic,  we  have 
the  equations 

but  the  volumes  at  A  and  D  are  equal,  as  are  also  the  volumes 
at  B  and  C;  consequently  by  division 

Zi       Z«. 

TC  "=  zy 

consequently 

and  the  expression  for  efficiency  becomes 


-(-~j     (is?) 

which  shows  that  the  efficiency  depends  only  on  the  compression 
before  explosion. 

For  example,  if  the  volume  of  the  clearance  or  compression 
space  is  one-third  of  the  piston  displacement,  so  that  vd  is  one- 
fourth  of  vel  then  the  efficiency  is 


*•         --          =0.43. 
The  pressure  at  the  end  of  compression  is 


GAS-ENGINES    WITH    COMPRESSION    IN   THE  CYLINDER   313 

pounds  absolute,  or  88.4  pounds  by  the  gauge.  The  calculated 
efficiency  is  therefore  not  much  less  than  the  efficiencies  found  for 
other  examples;  it  is  notable  that  the  efficiency  is  nearly  the 
same  as  that  calculated  on  page  307  for  an  engine  with  separate 
compression  to  90  pounds  by  the  gauge.  For  the  case  in  hand, 
however,  the  pressure  after  explosion,  which  depends  on  the 
temperature,  may  exceed  300  pounds  per  square  inch. 

The  diagrams  from  engines  of  this  type*  resemble  Fig.  72, 


FIG.  72. 

which  was  taken  from  an  Otto  engine  in  the  laboratory  of  the 
Massachusetts  Institute  of  Technology.  During  the  filling 
stroke,  the  pressure  in  the  cylinder  is  less  than  that  of  the  atmos- 
phere; the  charge  is  ignited  just  before  the  end  of  the  compression 
stroke,  and  the  explosion  though  rapid  is  not  instantaneous, 
as  is  indicated  by  the  rounding  of  the  corners  of  the  diagram 
at  both  the  bottom  and  the  top  of  the  explosion  line,  and  by 
the  leaning  of  that  line  to  the  right.  Release  occurs  before  the 
end  of  the  stroke,  and  there  is  considerable  back  pressure  during 
the  exhaust  stroke.  The  scale  of  the  diagram  is  150  pounds  to 
the  inch,  and  the  maximum  pressure  is  251  pounds.  The  atmos- 
pheric line  is  omitted  to  avoid  confusion. 

In  order  to  show  clearly  the  conditions  during  the  exhaust 
and  filling  strokes,  the  diagram  Fig.  73  was  taken  with  a  scale 

*  A  description  of  a  four-cycle  gas-engine  will  be  found  on  page  337,  and  may 
DC  read  for  the  first  time  in  this  connection. 


314 


INTERNAL-COMBUSTION    ENGINES 


of  20  to  the  inch,  and  with  a  stop  to  limit  the  rise  of  the  indicator- 
piston;  the  upper  part  of  the  diagram  consequently  does  not 
appear  in  the  figure.  The  mean  back-pressure  is  about  five 
pounds,  and  the  reduction  of  pressure  in  the  cylinder  is  between 


FIG.  73. 

three  and  four  pounds  below  the  atmosphere.  Reference  to 
the  influence  of  the  negative  area  of  Fig.  73  on  the  effective 
indicated  horse-power  will  be  made  later. 

The  compression  line  does  not  differ  very  much  in  appearance 
or  in  reality  from  an  adiabatic  line  from  air,  though  the  air  may 
be  expected  to  receive  heat  from  the  walls  of  the  cylinder  during 
the  first  part  of  the  compression  stroke,  and  may  part  with  heat 
during  the  latter  part.  The  expansion  line  has  a  resemblance 
to  the  adiabatic  line  for  air,  but  is  usually  less  steep,  especially 
for  large  engines;  but  in  reality  the  conditions  in  the  cylinder 
are  very  different,  for  the  combustion  does  not  cease  at  the  max- 
imum pressure,  but  continues  more  or  less  during  the  expansion 
stroke,  and  may  extend  to  the  release;  and  at  the  same  time 
heat  is  taken  up  energetically  by  the  walls  of  the  cylinder,  which 
are  cooled  by  a  water-jacket  to  avoid  overheating.  These  two 
effects,  after-burning  and  loss  of  heat  to  the  water-jacket,  deter- 
mine the  form  of  the  expansion  line  and  its  resemblance  to  an 
adiabatic  line. 

Characteristics  of  Gases.  —  There  are  three  distinct  kinds  of 
gases  used  in  gas-engines:  (i)  illuminating-gas,  (2)  producer- 
gas,  (3)  blast-furnace  gas.  Each  class  has  fairly  well-marked 
characteristics,  though  there  is  considerable  variation  in  a  class. 
The  greatest  variation  is  liable  to  be  found  in  blast-furnace 
gas,  since  the  metallurgical  operations  are  of  the  first  importance, 


CHARACTERISTICS    OF   GASES 


and,  if  the  gas  is  to  be  used  for  generating  power,  the  engines 
and  adjuncts  must  be  adapted  to  the  conditions.  Producer- 
gas  is  made  from  coke,  anthracite,  or  from  non-caking  bituminous 
coal,  and  consists  mainly  of  hydrogen  and  carbon  monoxide,  diluted 
with  the  nitrogen  of  the  air,  together  with  five  or  ten  per  cent 
of  carbon  dioxide  and  a  small  percentage  of  hydrocarbons  espe- 
cially when  bituminous  coal  is  used.  Illuminating- gas  is  now 
commonly  made  by  the  water-gas  process,  which  yields  a  gas  not 
very  unlike  producer-gas,  but  that  gas  is  enriched  with  hydro- 
carbons of  varying  composition;  formerly  illuminating-gas  was 
distilled  from  gas-coal,  which  was  a  rich  bituminous  coal  yielding 
a  large  percentage  of  hydrocarbons  when  distilled. 

The  general  characteristics  of  illuminating-gas  are  represented 
by  the  following  analysis  of  Manchester  coal-gas  quoted  from 
the  first  edition  of  Clerk's  Gas  Engine,  and  used  by  him  to 
investigate  the  effect  of  combustion  on  the  volume  of  the  gas. 

ANALYSIS   OF  MANCHESTER   COAL-GAS.     (Bunsen  and  Roscoe.) 


Vols. 

Vols.  O  required 
for 
Combustion. 

Products. 
Vols. 

Hydrogen  H 

4*    <?8 

22  .  7Q 

45.58,  H2O 

Methane,  CH4    

74.0 

60.8 

104.7,    c°2  &H2O 

Carbon  monoxide,  CO     .    . 
Ethylene,  C2H4 

6.64 
4.08 

3-32 
12  .24 

6.64,  C02 
16.32,  CO2  &H2O 

Tetrylene,  C4H8     
Sulphuretted  hydrogen,  H2S 

2.38 

0.29 

2    46 

14.28 
0-43 

19.04,  CO2&H2O2 
0.58,  H2O  &SO2 

2  .46 

Carbon  dioxide     CO2 

7    67 

3.67 

Total    

100.00 

122.86  O 

198.99,  CO2,H2O&SO2 

An  analysis  of  illuminating- gas  made  by  the  water-gas  process 
at  Boston  gave:  Hydrogen  27.9,  methane  28.9,  carbon  monoxide 
25=3,  carbon  dioxide  1.9,  hydrocarbons  12.0,  nitrogen  3.0,  oxygen 
i.o;  the  analysis  being  only  proximate  does  not  allow  of  a  calcu- 
lation of  the  oxygen  required  for  combustion. 

The  following  composition  of  producer-gas  was  taken  from  a 
report  of  tests  on  a  gas-engine  by  Professor  Meyer,  for  which 


INTERNAL-COMBUSTION    ENGINES 


COMPOSITION   OF  PRODUCER-GAS. 


Vols. 

Vols.  of 
Oxygen  for 
Combustion. 

Products 
Vols. 

Hydrogen  H 

1  •?    7 

6  8 

n  7  HoO 

Methane,  CH4 

O   7 

i  .  4 

2.1,  CO2  &  H2O 

Carbon  monoxide,  CO    .... 
Carbon  dioxide>  CO2 

24.6 

6  < 

12.3 
o 

24.6,  C02 
6.<t,  CO, 

Oxygen,  O     

.  f 

o 

o.q,  O 

Nitrogen,  N 

fA      O 

o 

?A  o,  N 

TOO 

20.5 

101.4 

details  are  given  on  page  350.  Eight  analyses  are  given  in  the 
original  paper,  which  are  here  averaged. 

Rich  non-caking  bituminous  coals  may  show  a  considerably 
larger  proportion  of  hydrogen. 

In  a  paper  on  the  use  of  blast-furnace  gas  Mr.  Bryan  Donkin 
gives  the  composition  of  gases  from  five  furnaces  in  England, 
Scotland,  and  Germany,  from  which  the  average  values  in  the 
following  table  were  deduced: 

COMPOSITION   OF   BLAST-FURNACE   GAS. 


Vols. 

Vols.  of 
Oxygen  for 
Combustion. 

Products. 
Vols. 

Hydrogen,  H    .        .    .        .    . 

2  .  S 

1  .  3 

2.«>.      H2O 

Carbon  monoxide,  CO   .... 
Carbon  dioxide,  CO2  . 

2Q.I 

7   O 

19.6 
o 

29.1,  CO2 
7.0,  CO« 

Nitrogen,  N  

61.4 

o 

61.4,  N 

100 

20.9 

100 

Not  only  is  there  much  variation  in  the  composition  of  gases 
from  different  blast-furnaces,  but  the  variation  with  the  progress 
of  the  metallurgical  operations  is  so  marked  that  it  is  customary 
to  mingle  the  gases  from  several  furnaces  in  order  to  insure 
that  the  gas  is  proper  for  use  in  gas-engines. 


CHARACTERISTICS    OF    GASES  317 

The  amounts  of  oxygen  required  for  the  combustion  of  a  given 
volume  of  any  gas  can  be  computed  from  the  formulae  rep- 
resenting the  chemical  changes  accompanying  combustion, 
together  with  the  fact  that  a  compound  gas  occupies  two  volumes, 
if  measured  on  the  same  volumetric  scale  as  the  component 
gases.  Thus  two  volumes  of  hydrogen  with  one  volume  of 
oxygen  unite  to  form  superheated  steam  as  represented  by  the 

formula 

2H  +  O  =  H20, 

and  the  three  volumes  after  combustion  and  reduction  to  the 
original  temperature  are  reduced  to  two  volumes;  in  this  case, 
to  have  the  statement  hold,  the  original  temperature  would  need 
to  be  very  high,  to  avoid  condensation  of  the  steam  into  water. 
But  in  the  application  to  gas-engines  this  leads  to  no  inconven- 
ience, because  the  gases  after  combustion  remain  at  a  high  tem- 
perature till  they  are  exhausted,  and  the  laws  of  gases  can  be 
assumed  to  hold  approximately.  A  compound  gas  like  methane 
•can  be  computed  as  follows: 

CH4  +  40  =  C02  +  2H20. 

Since  the  compound  gas  methane  occupies  two  volumes  and 
requires  four  volumes  of  oxygen,  it  is  clear  that  each  cubic  foot 
of  that  gas  will  demand  two  cubic  feet  of  oxygen;  the  total  volume 
may  be  reckoned  as  six  before  combustion,  and  in  like  manner 
there  will  be  six  volumes  after  combustion,  namely,  two  of 
carbon  dioxide  and  four  of  steam. 

In  this  way  the  oxygen  required  for  combustion  of  the  three 
kinds  of  gas  for  which  the  compositions  are  given,  has  been 
computed,  and  also  the  volumes  after  combustion.  For  coal- 
gas  the  contraction  due  to  the  combustion  of  hydrogen  and 
carbon  monoxide  is  very  nearly  compensated  by  the  expansion 
due  to  the  breaking  up  and  combustion  of  the  hydrocarbons. 
A  similar  result  may  be  expected  for  any  illuminating-gas.  On 
the  other  hand,  producer-gas  if  burned  in  oxygen  would  show  a 
contraction  of 


120.5  120 


3i 8  INTERNAL-COMBUSTION    ENGINES 

but  in  practice  the  producer-gas  is  mixed  with  1.3  to  1.5  of  its 
volume  of  air,  so  that  the  contraction  of  19  volumes  takes  place 
in  230  to  250  volumes,  and  thus  is  therefore  of  7 J  to  8  per  cent 
contraction. 

Clearly  this  matter  has  to  do  with  the  question  raised  on 
page  306,  as  to  the  reliance  to  be  placed  on  the  ideal  efficiencies 
which  assume  heating  of  air  instead  of  combustion  of  fuel. 
For  illuminating-gas  that  assumption  appears  unobjectionable, 
and  for  producer-gas  the  discrepancy  is  not  so  great  as  to 
destroy  the  value  of  the  method. 

Temperature  after  Explosion.  —  The  most  difficult  question 
concerning  the  theoretical  thermal  efficiency  of  gas-engines  is 
the  determination  of  the  temperature  after  explosion.  Direct 
determination  is  difficult  both  on  account  of  the  high  tempera- 
ture and  the  very  short  interval  of  time  during  which  the  maxi- 
mum temperature  can  be  considered  to  exist. 

A  comparatively  simple  calculation  of  the  temperature  after 
explosion  can  be  made  from  a  diagram  like  Fig.  72,  if  the  com- 
pression can  be  assumed  to  be  adiabatic,  and  if  the  laws  of 
perfect  gases  can  be  applied.  The  pressure  on  the  compression 
line  measured  on  an  ordinate  through  the  point  a  of  maximum 
pressure,  is  61  pounds,  or  75.7  pounds  absolute.  If  the  tem- 
perature of  the  gases  in  the  cylinder  at  atmospheric  pressure  is 
taken  to  be  70  degrees,  adiabatic  compression  gives  approxi- 
mately 

0.4 

Td= (70+460)  (^)"4=847°. 

\i4.7/ 

The  maximum  pressure  after  explosion  is  251  pounds,  or  about 
266  pounds  absolute.  If  the  temperature  at  constant  volume 
is  assumed  to  be  proportional  to  the  absolute  pressure,  we  have 

847  X  I—  =  2975, 

or  about  2500°  F.  This  result,  which  depends  on  the  assumption 
that  the  properties  of  the  charge  in  the  cylinder  of  a  gas-engine 


AFTER    BURNING 


3*9 


are  and  remain  the  same  as  those  of  gases  at  ordinary  tempera- 
tures, can  be  taken  as  a  first  approximation  only. 

In  connection  with  tests  on  a  gas-engine  (see  page  350)  using 
illuminating-gas,  Professor  Meyer  makes  a  careful  investigation 
of  the  temperature  which  might  be  developed  in  the  cylinder 
of  a  gas-engine  if  the  charge  were  completely  burned  in  a  non- 
conducting cylinder.  The  results  only  will  be  quoted  here. 
The  composition  of  the  gas  will  be  found  on  page  316,  from 
which  it  appears  that  it  was  probably  coal-gas  resembling 
Manchester  gas,  and  not  differing  very  radically  from  Boston 
gas,  by  use  of  which  Fig.  72  was  obtained.  The  pressure  at 
the  end  of  compression  was  69  pounds  by  the  gauge,  and  after 
explosion  was  220  pounds,  so  that  the  conditions  were  not  very 
different  from  those  of  Fig.  72,  except  that  the  pressure  on  the 
compression  line  is  not  on  the  ordinate  for  measuring  the  max- 
imum pressure,  and  therefore  the  parallel  calculation  cannot  be 
made. 

On  the  assumption  of  constant  specific  heats  Professor  Meyer 
finds  that  complete  combustion  should  give  4250°  F.  in  a  non- 
conducting cylinder,  but  using  Mallard  and  Le  Chatelier's 
equation  for  specific  heats  at  high  temperatures  he  gets  3330°  F. 
Those  experimenters  report  that  dissociation  of  carbon  monoxide 
begins  at  about  3200°  F.,  and  of  steam  at  about  4500°  F.;  but 
the  dissociation  is  slight  at  those  temperatures.  Though  the 
subject  is  still  obscure,  it  appears  fair  to  assume  that  the  failure 
to  reach  the  temperatures  which  can  be  computed  for  complete 
combustion,  can  be  charged  in  part  to  suppression  of  combustion 
on  account  of  the  high  temperature  in  the  cylinder. 

After  Burning.  —  Accompanying  the  suppression  of  heat  on 
account  of  the  approach  to  the  temperature  of  dissociation  is 
the  development  of  heat  during  expansion  which  extends  in  some 
cases  to  release,  as  is  indicated  by  a  flicker  of  flame  into  the 
exhaust;  explosions  in  the  mufflers  of  automobiles  are  attributable 
to  this  action.  The  fact  that  the  expansion  curve  approaches 
the  adiabatic  line  during  expansion  is  indirect  evidence  of  after- 
turning,  because  the  water-jacket  withdraws  heat  at  the  same 


320  INTERNAL-COMBUSTION    ENGINES 

time.  The  actual  expansion  line  is  less  steep  than  the  adiabatic 
for  gas,  and  for  large  gas-engines  can  approach  the  condition 
represented  by  the  equation 

pv  l'2  =  const. ; 

but  a  part  of  this  action  can  be  attributed  to  the  presence  of 
carbon  monoxide  and  steam  in  the  products  of  combustion,  which 
may  reduce  the  exponent  of  the  adiabatic  line  from  1.405  to  1.37. 

Water-jackets.  —  All  except  very  small  internal-combustion 
engines  have  the  heads  and  barrels  of  the  cylinder  cooled  by 
water-jackets;  large  engines  commonly  have  the  pistons  cooled 
with  water,  and  double-acting  engines  have  the  piston-rods  and 
stuffing-boxes  cooled.  Not  uncommonly  the  valves  of  large 
engines  are  cooled,  and  if  such  engines  use  rich  gases,  extra 
cooling  surface  is  provided  in  the  charging  space  or  cartridge 
chamber;  the  latter  device  is  to  avoid  pre-ignition,  and  the 
former  is  in  part  for  the  same  purpose. 

Primarily,  water-jackets  are  to  protect  the  metal  of  the  cylinder 
and  to  make  lubrication  possible.  The  use  of  jackets  and  other 
cooling  devices  has  been  considered  a  mechanical  necessity,  which 
many  inventors  have  sought  to  avoid;  but  it  appears  likely  that 
it  is  only  a  question  whether  the  heat  shall  be  withdrawn  by  a 
water-jacket,  or  whether  the  heat  shall  be  suppressed  by  dissocia- 
tion and  thrown  .out  in  the  exhaust.  Large  engines,  which  have 
less  exposed  area  per  cubic  foot  of  cylinder  contents,  show  a  less 
percentage  of  heat  withdrawn  by  the  jacket,  but  a  larger  per- 
centage thrown  on  in  the  exhaust;  the  balance  is,  however,  in 
favor  of  large  engines  which  show  a  better  economy. 

Economy  and  Efficiency.  —  It  is  customary  and  altogether 
desirable  to  rate  the  economy  of  gas-engines  and  other  internal - 
combustion  engines  in  thermal  units  per  horse-power  per  minute ; 
this  was  found  to  be  desirable,  if  not  necessary,  for  studying 
the  means  of  improving  the  performance  of  steam-engines.  But 
as  steam-engines  are  commonly  rated  in  terms  of  steam  per 
horse-power  per  hour,  so  also  gas-engines  have  been  rated  in 
terms  of  cubic  feet  of  gas  per  horse-power  per  hour,  and  gasoline- 


ECONOMY    AND    EFFICIENCY  321 

and  oil-engines  have  been  rated  in  pounds  of  fuel  per  horse- 
power per  hour.  The  variation  in  the  fuel  used  for  such  engines 
makes  the  secondary  methods  less  satisfactory  than  rating  engines 
on  steam-consumption,  so  that  it  should  be  employed  only  when 
the  calorific  capacity  of  the  fuel  cannot  be  determined  or 
estimated. 

Since  the  heat-equivalent  of  a  horse-power  is  42.42  thermal 
units  per  minute,  the  actual  thermal  efficiency  of  an  internal- 
combustion  engine  can  be  determined  by  dividing  that  figure 
by  the  thermal  units  consumed  by  the  engine  per  horse-power 
per  minute.  For  example,  the  engine  tested  by  Professor  Meyer 
used  about  170  thermal  units  per  horse-power  per  minute, 
and  its  thermal  efficiency  was  0.25,  using  the  indicated  horse- 
power. The  ratio  of  the  cartridge  space  to  the  whole  volume 

was    — — ,  so  that  equation  (187)  gives  in  this  case  0.42  for  the 
3-^4 

nominal  theoretical  efficiency;  consequently  the  ratio  of  the 
efficiencies  is  nearly  0.60. 

By  a  somewhat  intricate  method  Professor  Meyer  computed 
the  efficiency  for  two  tests  on  the  engine  for  which  details  are 
given  on  page  350,  on  the  assumption  that  complete  combustion 
occurred  in  a  non-conducting  cylinder.  The  ratio  of  gas  to  air 
in  one  test  was  one  to  8.9,  and  in  the  other  one  to  12.  Assuming 
that  the  specific  heat  of  the  mixture  in  the  cylinder  before  and 
after  explosion,  remained  constant,  he  found  for  the  first  test 
an  efficiency  of  0.398,  and  for  the  second  0.403 ;  but  making  use 
of  Mallard  and  Le  Chatelier's  investigations  on  specific  heats  at 
high  temperatures,  he  found  for  the  efficiencies  0.297  and  0.318. 
The  values  for  constant  specific  heat  differ  but  little  from  the 
nominal  theoretical  efficiency ;  in  fact,  if  the  exponent  be  reduced 
from  0.405  to  0.38,  the  nominal  efficiency  becomes  0.40,  which 
is  a  very  close  coincidence.  But  the  efficiencies  computed  from 
the  heat-consumptions  for  these  two  tests  are  0.253  and  0.249. 
If  then  the  nominal  theoretical  efficiency,  or  the  efficiency  which 
Professor  Meyer  calculated  on  assumption  of  constant  specific 


322 


INTERNAL-COMBUSTION    ENGINES 


heat,  be  taken  as  the  basis  of  comparison,  the  engine  gave  for 
the  ratio  of  actual  to  theoretical  efficiency, 

0.253  -?-  0.398  =  0.64,  or  0.249  -f-  0.403  =*  0.62. 
If,  however,  we  take  his  second  values  with  variable  specific  heat, 
we  have 

0.253  -s-  0.297  =  °-^5)  or  0.249  ~*~  °-31^  =  0-78. 

Professor  Meyer  uses  these  computations  to  emphasize  the 
importance  of  better  knowledge  of  the  properties  of  the  working 
substance  in  the  cylinder  of  an  internal-combustion  engine; 
because,  if  the  nominal  theoretical  efficiency  be  taken  for  the 
basis  of  comparison,  there  appears  to  be  room  for  material 
improvement  in  the  economy  of  the  engine;  whereas,  if  the 
second  set  of  computations  is  taken  as  the  basis,  there  is  little 
prospect  of  improvement.  In  conclusion,  attention  is  called  to 
the  fact  that  these  tests  were  on  a  small  engine  which  developed 
only  ten  brake  horse-power. 

In  the  discussion  of  efficiency  we  have  thus  far  made  use  of  the 
heat-consumption  per  indicated  horse-power,  which  is  proper, 
because  the  fluid  efficiency  (or  the  efficiency  of  the  action  of  the 
working  substance)  should  for  this  purpose  be  preserved  from 
confusion  with  the  friction  and  mechanical  efficiency  of  the 
engine.  For  the  same  reason,  and  also  because  the  power  of  a 
steam-engine  can  be  determined  satisfactorily  by  the  indicator, 
we  used  indicated  horse-power  in  the  discussion  of  steam-engine 
economy.  There  is,  however,  a  reason  why  the  indicated  power 
is  not  a  satisfactory  basis  for  the  discussion  of  the  economy  of 
internal -combustion  engines,  namely,  the  fact  that  a  series  of 
successive  diagrams  taken  without  removing  the  pencil  from  the 
paper  on  the  indicator  drum,  will  show  a  wide  dispersion,  due 
to  the  varying  explosive  action  in  the  cylinder  even  when  con- 
ditions are  most  favorable.  When  the  engine  is  governed  by 
omitting  explosions,  this  difficulty  is  much  aggravated  on  account 
of  the  negative  work  of  idly  drawing  in,  compressing,  and  expel- 
ling air. 

Fig.  74  shows  a  diagram  taken  from  the  same  engine  as  Fig. 
72,  page  313,  but  with  a  fifty-pound  spring  and  a  stop  to  prevent 


ECONOMY   AND    EFFICIENCY 


323 


the  indicator  piston  from  rising  too  high  which  exhibits  the 
effects  of  an  idle  cycle  and  other  features.  A  portion  of  the 
expansion  curve  is  shown,  with  oscillations  due  to  the  piston 
suddenly  leaving  the  stop.  The  exhaust  of  the  spent  gases  is 


FIG.  74. 

shown  by  the  curve  ab,  after  which  the  engine  draws  a  charge 
of  air  (without  gas)  and  compresses  it  on  the  upper  curve  from 
c  to  d\  on  the  return  stroke  the  indicator  follows  the  lower 
curve  from  d  to  c,  so  that  the  loop  represents  work  done  by  the 
engine;  finally  the  air  is  exhausted,  while  the  indicator  draws 
the  line  ce.  To  explain  the  difference  between  the  exhaust  lines 
ab  and  ce  with  spent  gas  and  with  air  only,  it  may  be  noted  that 
there  is  a  marked  drooping  of  the  exhaust  line  a  at  about  one- 
fifth  of  the  stroke  from  b',  this  feature  is  more  marked  in  Fig.  73, 
which  shows  the  exhaust  stroke  to  a  larger  scale.  This  droop 
may  be  attributed  to  the  inertia  of  the  column  of  gas  in  the 
exhaust  pipe;  the  smaller  volume  of  air  which  is  exhausted  with 
gradually  rising  pressure  does  not  happen  to  develop  this  feature 
in  such  a  way  as  to  produce  the  result  shown  in  Fig.  73.  This 
drop  of  pressure  in  the  exhaust  pipe  may  be  accentuated  by 
adjusting  the  length  of  the  exhaust  pipe  so  as  to  give  a  partial 
vacuum  just  before  the  engine  takes  its  next  charge;  when  this 
action  is  obtained,  the  air-valve  is  opened  before  the  gas-valve, 
and  fresh  air  is  drawn  through  the  cylinder  to  produce  a  scav- 
enging effect  before  the  engine  takes  a  new  charge.  At  one 


324  INTERNAL-COMBUSTION    ENGINES 

time  considerable  importance  was  given  to  scavenging  to  clear 
out  spent  gas,  but  it  attracts  less  importance  now  for  four-cycle 
engines. 

In  indicating  a  gas-engine,  allowance  is,  of  course,  made  for 
the  negative  work  of  exhaust  and  filling;  if  an  explosion  is  missed, 
allowance  for  the  negative  work  for  the  operation  shown  on 
Fig.  74  should  be  made  for  each  idle  cycle,  and  when  the  engine 
has  only  a  few  working  cycles  the  error  of  not  taking  proper 
account  of  the  negative  work  may  be  very  large.  This  is,  of 
course,  another  reason  why  comparisons  are  best  based  on  brake 
horse-power.  As  can  be  seen  from  Table  XXXV  on  page  350, 
the  mechanical  efficiency  may  range  from  60  per  cent  to  80 
per  cent,  depending  mainly  on  the  power  developed;  these  figures 
are  for  continuous  explosions,  and  the  efficiency  is  liable  to  be 
much  reduced  if  explosions  are  omitted  at  reduced  power. 

Two-cycle  engines  commonly  have  a  compression  pump 
which  supplies  the  mixture  of  gas  and  air  at  a  pressure  of  five  or 
ten  pounds  above  the  atmosphere ;  in  such  case  the  work  of  com- 
pression must  be  determined  separately  and  allowed  for,  in  the 
measurement  of  the  indicated  horse-power. 

Valve-Gear.  —  The  supply  and  exhaust  parts  for  an  internal- 
combustion  engine  are  always  separate, -so  that  there  are  at 
least  two  valves  (or  the  equivalent)  for  each  working  end  of  a 
cylinder;  there  is  also  for  a  gas-engine  a  separate  valve  for 
admitting  or  controlling  the  supply  of  gas.  The  valves  are 
usually  plain  disk  or  mushroom  valves  with  mitered  seats;  in 
some  cases  double-beat  valves  are  used  on  large  engines.  Very 
commonly  two-cycle  engines  exhaust  through  ports  cut  through 
the  cylinder  walls  and  opened  by  the  piston  itself,  wrhich  over- 
runs them  near  the  end  of  its  stroke;  in  at  least  one  case  the 
exhaust-valves  of  a  four-cycle  engine  are  water-cooled  hollow 
piston-valves,  but  that  construction  appears  to  be  exceptional. 

The  exhaust- valves  are  always  positively  controlled,  since  they 
must  remain  closed  against  pressure  in  the  cylinder  until  the 
proper  time.  The  inlet  valves  may  be  operated  by  the  pressure 
of  the  operating  fluid,  opening  during  the  suction  stroke  and 


STARTING   DEVICES  325 

remaining  closed  during  the  compression,  expansion,  and  exhaust 
strokes;  but  very  commonly  the  admission  valves  both  for  air 
and  for  gas  (when  the  latter  are  separate)  are  positively  con- 
trolled, and  for  very  high  speeds  this  action  is  necessary. 

From  what  has  been  said,  it  will  be  evident  that  the  general 
problem  of  the  design  of  the  valve-gear  for  an. internal-combus- 
tion engine  resembles  that  for  a  four- valve  steam-engine,  espe- 
cially that  type  of  steam-engine  valve-gear  which  uses  simple 
lift-valves.  The  solution  which  is  most  evident  and  most  com- 
monly chosen  is  some  form  of  cam- gear;  usually  the  valves  are 
held  shut  by  springs,  and  are  opened  by  cams  on  a  cam-shaft 
either  directly  or  through  linkages.  This  cam-shaft  is  conven- 
iently placed  parallel  to  the  axis  of  the  cylinder  and  driven  from 
the  main  shaft  through  bevel-gears;  the  four-cycle  engine  has 
the  gear  in  the  ratio  of  one  to  two,  so  that  the  cam-shaft  makes 
one  revolution  for  two  revolutions  of  the  engine  in  order  to 
properly  time  the  four  principal  operations  of  the  cycle.  The 
spring  closing  a  valve  must  be  properly  designed  not  only  to 
give  the  required  pressure  to  hold  the  valve  shut,  but  to  provide 
the  proper  acceleration  so  that  the  valves  shall  remain  under 
the  control  of  the  cam  when  closing.  The  cam-shaft,  in  addi- 
tion to  the  cams  for  the  normal  action  of  the  engine,  carries  cams 
which  facilitate  starting  the  engine. 

Starting  Devices.  —  Since  an  internal-combustion  engine  must 
do  the  work  of  drawing  in  and  compressing  its  charge  before 
energy  is  developed  by  explosion,  some  special  device  is  required 
to  start  such  an  engine,  involving  the  use  of  power  from  an 
external  source.  It  is  seldom  if  ever  convenient  to  apply  power 
sufficient  to  start  an  engine  under  its  load,  and  consequently 
there  must  be  some  disengagement  gear  to  allow  the  engine  to 
start  without  load,  except  in  cases  where  the  load  is  developed 
only  as  the  engine  comes  up  to  speed. 

A  small  engine  can  be  started  by  hand,  by  turning  the  fly- 
wheel or  by  working  a  special  hand-gear;  the  latter  should  have 
a  ratchet  or  clutch  which  will  release  or  throw  it  out  of  gear 
as  soon  as  the  engine  starts.  The  engine  is  driven  by  hand  until 


326  INTERNAL-COMBUSTION    ENGINES 

the  operations  of  charging,  compressing,  and  igniting  are  per- 
formed, whereupon  the  engine  should  start  promptly.  Except 
for  very  small  sizes,  there  is  a  special  cam  that  may  be  thrown 
into  action,  and  which  holds  the  exhaust-valve  open  till  the 
piston  has  completed  about  half  the  compression  stroke,  during 
which  the  charge  is  partially  wasted;  by  this  device  the  labor  of 
compression  is  much  reduced.  When  an  engine  is  started  in 
this  manner  the  ignition  should  be  delayed  until  the  piston  is 
past  the  dead-point,  otherwise  the  engine  is  liable  to  start  back- 
ward. The  disengagement  clutch  will  not  act  in  such  case, 
and  there  is  great  danger  of  an  accident. 

When  electric  or  other  external  power  can  be  substituted  for 
hand-power,  this  method  can  be  used  for  starting  engines  of 
large  size. 

A  very  common  device  is  to  start  the  engine  with  compressed 
air  from  a  tank  at  a  pressure  of  100  to  200  pounds  per  square 
inch.  This  air  is  supplied  to  the  tank  by  a  pump  driven  by 
the  engine  when  necessary0  To  start  the  engine  the  cylinder  is 
disconnected  temporarily  from  the  ordinary  gas  and  air  supply, 
and  is  worked  like  a  compressed-air  engine  until  well  under 
way,  whereupon  the  compressed  air  is  shut  off  and  the  normal 
action  is  restored.  The  air  can  be  supplied  from  the  tank  by 
valves  controlled  by  hand  or  by  a  special  gear.  If  the  engine 
has  more  than  one  cylinder,  compressed  air  may  be  supplied  to 
one  only,  and  the  other  cylinder  (or  cylinders)  may  act  in  the 
usual  manner,  except  that  the  compression  may  be  reduced  till 
the  engine  is  started. 

At  one  time  gas  was  withdrawn  from  the  cylinder  during  the 
compression  stroke,  and  stood  in  a  reservoir  to  be  used  for  start- 
ing. Such  gas  could  be  used  at  a  pressure  of  60  to  90  pounds, 
to  start  the  engine  as  just  described;  or  the  piston  could  be  set 
beyond  the  dead-point  ready  to  start,  gas  could  be  supplied 
under  pressure  and  ignited.  There  is,  of  course,  some  objection 
to  the  storage  of  explosive  mixtures,  though  there  is  no  reason 
why  the  reservoir  should  not  be  made  able  to  endure  an  explosion. 

Governing  and   Regulating.  —  There  are  four  ways  available 


GOVERNING   AND    REGULATING  327 

for  controlling  the  power  of  an  internal-combustion  engine:  (i) 
by  regulating  the  proportion  of  air  and  fuel,  (2)  by  regulating 
the  amount  of  air  and  fuel  without  changing  the  proportion, 
(3)  by  omitting  the  supply  of  fuel  during  a  part  of  the  cycles,  (4) 
delaying  ignition. 

(i )  Regulation  by  controlling  the  supply  of  fuel  is  the  normal 
method  for  engines  working  on  the  Joule  or  Brayton  cycle  with 
compression  in  a  separate  cylinder,  for  which  a  theoretical  dis- 
cussion is  given  on  page  305.  For  this  cycle  there  is  no  explo- 
sion, but  the  gaseous  or  liquid  fuel  can  be  burned  during  admis- 
sion in  any  proportion. 

The  Brayton  engine  had  a  double  control  for  variation  in 
load.  In  the  first  place  a  ball-governor  shortened  the  cut-off 
for  the  working  cylinder  when  the  speed  increased  on  account 
of  reduction  in  the  load;  this  had  the  effect  of  raising  the  pres- 
sure in  the  air  reservoir  into  which  the  air-pump  delivered,  since 
that  pump  delivered  nearly  the  same  weight  of  air  per  stroke 
under  all  conditions.  In  the  second  place,  there  was  an  arrange- 
ment for  shortening  the  stroke  of  the  little  oil-pump  when  the 
pressure  increased;  so  that  indirectly  the  amount  of  fuel  was 
proportioned  to  the  load.  A  similar  effect  was  produced  when 
the  engine  was  designed  to  use  gas. 

For  the  Diesel  motor,  to  be  described  later,  the  fuel  supply 
can  be  adjusted  to  the  power  demanded  for  all  conditions  of 
service.  » 

But  for  gas-engines  it  has  not  been  found  practicable  to  con- 
trol the  engine  by  regulating  the  mixture  of  gas  and  air  except 
within  narrow  ranges.  This  comes  from  the  fact  that  very  rich 
or  very  poor  mixtures  of  gas  and  air  will  not  explode.  Experi- 
ments at  the  Massachusetts  Institute  of  Technology  show  that 
illuminating-gas  will  explode  at  atmospheric  pressure  with 
the  ratio  of  gas  to  air  varying  from  1 115  to  i :  3.5.  Weaker  mix- 
tures can  be  exploded  in  a  gas-engine  after  compression.  Again, 
gas  may  be  supplied  in  such  a  way  that  the  mixture  near  the 
point  of  ignition  may  be  rich  enough  to  explode  promptly  and 
fire  the  remainder  of  the  charge.  The  ignition  of  weak  mix- 


328  INTERNAL-COMBUSTION    ENGINES 

tures  should  occur  before  the  end  of  the  compression  stroke,  so 
that  even  though  the  explosion  is  slow  it  may  be  completed  near 
the  beginning  of  the  working  stroke. 

The  tests  on  page  350  show  that  with  the  ratio  of  gas  to  air 
varying  from  i  :  8  to  i  :  12  the  power  may  vary  from  10  to  6 
brake  horse-power. 

This  discussion  of  the  possibility  of  varying  the  power  by 
varying  the  mixture  of  gas  and  air  would  appear  to  show  that 
for  many  purposes  that  should  be  a  practicable  way  of  governing 
a  gas-engine.  Nevertheless  it  is  used  very  little  if  at  all,  although 
it  was  tried  early. 

(2)  The  common  way  of  governing  large  gas-engines  is  to 
vary  the  supply  of  the  mixture  without  varying  its  proportions. 
There  are  two  ways  of  accomplishing  this :  in  the  first  place  the 
charge  may  be  throttled  so  that  a  less  weight  is  drawn  in  at  a 
lower  pressure;  in  the  second  place  the  admission  valve  may  be 
closed  before  the  end  of  the  filling  stroke,  thus  cutting  off  the 
supply.     The  effect  of  throttling  is  to  increase  to  a  marked  extent 
the  reduction  of  pressure  during  the  filling  stroke  with  a  corre- 
sponding increase  in  the  negative  work;  the  area  of  the  loop 
like  that  shown  by  Fig.  72,  page  313,  will  increase.     The  effect 
of  closing  the  inlet-valve  before  the  end  of  the  filling  stroke  is 
to  produce  a  diagram  similar  to  Fig.  70,  page  310.     The  charge 
is  drawn  in  at  a  pressure  a  little  below  that  of  the  atmosphere 
as  far  as  the  point  C;  then  the  piston  goes  on  to  the  end  of  the 
stroke  with  an  expansion  that  could  be  represented  by  produ- 
cing the  curve  DC]  the  return  stroke  produces  a  compression 
that  can  be  represented  by  retracing  the  produced  part  of  the 
curve  from  C  and  then  drawing  the  true  compression  curve 
CD.     In  practice  the  indicator  diagram  will  show  a  small  nega- 
tive work  due  to  the  expansion  and  compression  caused  by  the 
early  closing  of  the  supply- valve,  but  the  loss  on  that  account  is 
less  than  by  throttling. 

(3)  The  third  way  of  controlling  a  gas-engine  is  to  cut  off 
the  gas  supply  so  that  the  engine  draws  in  a  charge  of  air  only 
and  makes  an  idle  cycle,  represented  by  Fig.  74,  page  323.     At 


IGNITION  329 

small  power  the  negative  work  of  idle  cycles  very  much  reduces 
the  brake  economy  of  the  engine.  Now,  a  single-acting  four- 
cycle engine  has  only  one  working  stroke  in  four,  and  must  fur- 
nish between  times  the  work  of  expulsion,  filling,  and  compres- 
sion, and  even  with  a  very  heavy  fly-wheel  will  show  an  irregu- 
larity in  speed  of  revolution  that  is  very  objectionable  for  many 
purposes.  This  difficulty  is  very  much  increased  if  the  engine 
is  governed  by  omitting  explosions  on  the  hit-or-miss  principle. 

(4)  Delaying  ignition  is  one  of  the  favorite  ways  of  reducing 
the  power  of  automobile-engines  on  account  of  its  convenience; 
it  is  little  used  for  other  engines,  and  is  very  wasteful  of  fuel, 
as  there  is  not  time  for  proper  combustion. 

Ignition.  —  The  ignition  of  the  charge  may  be  produced  by 
one  of  three  methods:  (i)  by  an  electric  spark,  (2)  by  a  hot  tube, 
or  (3)  by  compression  in  a  hot  chamber. 

(i)  The  electric  spark  may  be  produced  in  one  of  two  ways, 
—  by  the  make-and-break  method,  or  by  the  jump-spark  method. 
For  the  first  method  a  movable  piece  is  worked  inside  the  cylin- 
der walls,  which  closes  a  primary  circuit  some  time  before  igni- 
tion is  desired;  the  slight  closing  spark  has  no  effect.  At  the 
proper  time  the  moving  mechanism  breaks  the  circuit,  and  a 
good  spark  is  made  between  the  terminals,  which  are  tipped 
with  platinum.  A  coil  in  the  circuit  intensifies  or  fattens  the 
opening  spark.  The  spark  obtained  by  this  method  is  likely 
to  be  better  than  the  jump-spark,  but  there  is  the  great  incon- 
venience of  a  moving  mechanism  in  a  cylinder  exposed  to  very 
high  pressure,  and  the  motion  must  be  communicated  by  a 
piece  which  enters  the  cylinder  through  a  stuffing-box. 

The  jump-spark  between  two  platinum  terminals  in  an  insu- 
lated spark-plug,  screwed  through  the  cylinder  wall,  is  a  high- 
tension  spark  in  a  secondary  circuit  made  by  a  circuit-breaker 
outside  of  the  cylinder.  The  movable  parts  in  this  case  are  under 
observation  and  can  be  adjusted,  and  the  spark-plug  can  be 
easily  withdrawn  for  examination  or  renewal.  Frequently  there 
are  two  plugs  that  can  be  worked  individually  or  together,  or 
both  make-and-break  and  jump-sparks  may  be  supplied. 


330  INTERNAL-COMBUSTION    ENGINES 

The  circuit  may  be  supplied  by  a  primary  battery,  or  may  be 
generated  by  a  small  dynamo  driven  by  the  engine,  or  may  be 
supplied  from  any  convenient  source.  When  a  dynamo  is  sup- 
plied, the  engine  is  usually  started  by  aid  of  a  battery. 

The  electric  method  of  ignition  was  the  earliest  used  in  the 
history  of  the  gas-engine,  and  though  it  was  at  one  time  neglected, 
now  tends  to  become  universal. 

(2)  The  hot  tube  requires  only  a  small  iron  tube,  which  is 
kept  red-hot  by  a  Bunsen  burner  or  other  heating  flame.     The 
tube  comes  out  horizontally  from  the  cylinder,  and  sometimes 
is  turned  upward  for  convenience  in  heating.     At  the  proper 
time  the  explosive  mixture  in  the  cylinder  is  admitted  to  the 
tube  by  a  valve  which  is  worked  by  the  engine.     Sometimes 
the  tube  has  an  inlet- valve  at  the  outer  end  to  ventilate  the 
tube  with  air  drawn  in  during  the  filling  stroke.     This  method 
has   been  widely  used  in   Great   Britain,   where  the  electrical 
method  has  met  with  little  favor,  though  the  prejudice  against 
it  is  passing  away. 

(3)  Ignition  by  compressing  the  charge  in  a  hot  chamber  is 
used  exclusively  in  oil-engines,  and  is  an  ingenious  example  of 
taking  advantage  of  a  condition  that  at  first  sight  appears  to  be 
undesirable.     The  mixture  of  air  and  kerosene  oil  in  engines  of 
this  class  is  produced  by  spraying  oil  into  a  chamber  attached 
to  the  cylinder  and  unprovided  with  a  water-jacket,  so  that  it 
is  maintained  by  the  explosion  at  a  red  heat.     The  charge  thus 
produced  is  more  likely  to  be  exploded  than  a  mixture  of  gas 
and  air,  when  it  comes  in  contact  w  ith  a  hot  surface,  and  under  the 
conditions  stated  explosion  cannot  be  avoided.     Much  ingenuity 
has  been  expended  in  adjusting  sizes  and  proportions  of  parts,  and 
frequency  of  explosion,  to  obtain  the  explosion  when  it  is  desired. 

The  tendency  to  work  large  gas-engines  with  high  com- 
pression, in  order  to  obtain  great  power  without  undue  bulk 
and  cost,  is  likely  to  lead  to  the  danger  of  premature  explosion, 
especially  when  rich  gas  is  used.  Any  projecting  part  (a  bolt- 
head  or  part  of  a  valve)  may  become  sufficiently  heated  to 
cause  explosion;  or  a  spongy  spot  in  a  casting  may  act  in  the 


GAS-PRODUCERS  331 

same  way.  Premature  explosion  in  a  small  engine  after  it  is 
started  may  be  an  inconvenience,  but  in  a  large  engine  it  may 
lead  to  an  accident. 

Gas- Producers.  —  A  gas-producer  is  essentially  a  furnace 
which  burns  coal  or  other  fuel  with  a  restricted  air  supply,  so 
that  the  combustion  is  incomplete  and  the  products  of  combus- 
tion are  capable  of  further  combustion.  In  its  simplest  form  a 
gas-producer  will  deliver  a  mixture  of  carbon  monoxide  and 
nitrogen  together  with  small  percentages  of  carbon  dioxide  oxygen 
and  hydrogen.  If  a  proper  proportion  of  steam  is  supplied  with 
the  air,  its  decomposition  in  contact  with  the  incandescent  fuel 
will  yield  free  hydrogen,  and  the  gas  will  give  a  higher  pressure 
when  exploded,  and  develop  more  power  in  the  engine  cylinder. 

When  gas  is  produced  on  a  large  scale  in  a  stationary  plant, 
intricate  devices  may  be  used  to  rectify  the  gas  and  save  the 
by-products,  which  are  likely  to  be  so  important  as  to  control 
the  methods  employed.  The  most  important  by-product  at 
the  present  time  appears  to  be  ammonium  sulphate,  which  is 
used  as  a  fertilizer,  and  for  this  reason  a  coal  is  preferred  which 
has  a  relatively  large  proportion  of  nitrogen.  At  a  certain 
station  a  coal  containing  three  per  ctnt  of  nitrogen  produced 
crude  ammonium  sulphate  that  could  be  sold  for  half  the  price 
of  the  coal.  This  branch  of  chemical  engineering  is  a  specialty 
of  growing  importance,  and  an  adequate  treatment  of  it  would 
demand  a  separate  treatise.  Such  plants,  especially  when  the 
gas  is  used  for  heating  furnaces  as  well  as  for  power,  are  worked 
under  pressure,  the  air  and  steam  being  blown  into  the  furnace. 

When  a  producer  supplies  gas  for  power  only,  there  is  a  great 
gain  in  simplicity  and  in  certainty  of  control,  if  the  producer  is 
worked  by  suction,  the  engine  being  allowed  to  draw  its  charge 
directly  from  the  producer.  During  the  suction  stroke  there 
must  be  a  sufficient  vacuum  in  the  engine  cylinder  to  work  the 
producer;  this  amounts  to  about  two  pounds  below  the  atmos- 
phere. There  is  no  attempt  in  this  case  to  save  by-products, 
and  the  fuel  must  be  chosen  so  that  comparatively  simple  rectify- 
ing  devices  will  give  a  gas  that  will  not  clog  the  engine.  At 


332 


INTERNAL-COMBUSTION    ENGINES 


the  present  time  the  fuels  used  are  coke,  anthracite,  and  non- 
caking  bituminous  coal.  At  the  Louisiana  Purchase  Exposi- 
tion, at  St.  Louis  in  1904,  a  very  large  variety  of  fuels,  including 
caking  bituminous  coal  and  lignite,  were  used  in  an  experimental 
plant,  and  it  is  likely  that  all  kinds  of  fuel  will  eventually  be 
used  in  practice. 

Fig.  75  gives  the  section  of  a  Dowson  suction  producer,  in 
which  A  is  the  grate  carrying  a  deep  coal  fire;  at  B  is  the  charg- 
ing hopper  with  double  doors, 
so  that  the  vacuum  is  not  lost 
during  charging;  at  C  is  a 
vaporizer  filled  with  pieces  of 
fire-brick,  which  are  heated  by 
the  hot  gases  from  the  furnace; 
water  is  sprayed  on  to  the  fire- 
brick through  holes  in  a  circular 
water-pipe  D,  and  flashes  into 
steam  which  mingles  with  the 
air  supply;  the  air  for  com- 
bustion enters  at  jP,  and  passing 
through  the  vaporizer  is  charged 
with  steam  and  then  flows 
through  the  pipe  L  to  the  ash-pit.  In  the  normal  working 
of  the  engine  the  gas  passes  through  the  pipe  G  and  the 
water-seat  at  J  to  the  scrubber  K,  which  is  filled  with  coke 
sprayed  with  water.  From  K  the  gas  passes  directly  to 
the  engine.  To  start  the  producer,  kindling  is  laid  on  the 
grate  and  the  furnace  is  filled;  the  fire  is  lighted  through  a 
side  door,  and  air  is  blown  in  by  a  fan  driven  by  hand.  At 
first  the  gas  is  allowed  to  escape  through  the  pipe  /,  until  gas 
will  burn  well  at  the  testing-cock  at  H\  then  the  pipe  /  is  shut 
off,  and  the  gas  is  blown  through  the  scrubber  and  wasted  at  a 
pipe  near  the  engine  until  it  appears  to  be  in  good  condition 
when  tested  at  that  place.  The  engine  is  then  started  and  the 
fan  is  stopped. 

The  producer  described  is  intended  to  burn  coke  or  anthra- 


FIG.  75. 


OTHER    KINDS    OF   GAS  333 

cite;  those  that  burn  bituminous  coal  must  have  some  method 
of  dealing  with  tarry  matter.  Sometimes  this  is  accomplished 
by  passing  the  gas  through  a  sawdust  cleaner;  sometimes  a 
centrifugal  extractor  is  added.  Some  makers  remove  the  tar 
by  care  in  cooling  before  the  gas  comes  in  contact  with  water. 
Others  pass  the  distillate  through  the  fire,  and  thus  change  it 
into  light  gas  or  burn  it;  with  this  in  view,  some  producers  work 
with  a  down-draught.  It  is  probable  that  different  kinds  of 
fuel  will  need  different  treatments. 

Blast-furnace  Gas.  —  From  the  composition  of  blast-furnace 
gas  on  page  316,  it  is  evident  that  it  differs  from  producer- gas 
only  in  that  it  contains  very  little  hydrogen,  and  therefore  is 
like  the  gas  that  would  be  made  in  a  producer  working  without 
steam.  During  the  operation  of  the  furnace  the  composition 
is  liable  to  vary  and  the  gas  may  become  too  weak;  to  remedy 
this  difficulty,  it  is  desirable  to  mingle  the  gases  from  two  or 
more  furnaces.  Since  the  gas  available  from  a  furnace  may 
be  equivalent  to  2000  horse-power,  it  is  evident  that  installations 
to  develop  power  from  that  source  must  be  on  a  very  large 
scale. 

The  gas  from  a  blast-furnace  is  charged  with  a  large  amount 
of  dust,  some  of  which  is  metallic  oxide,  and  readily  falls  out, 
and  the  remainder  is  principally  silica  and  lime  which  is  very 
fine  and  light.  To  remove  this  fine  dust  the  gas  should  be 
passed  through  a  scrubber,  which  has  the  additional  advantage 
of  cooling  the  gas. 

Other  Kinds  of  Gas.  —  Any  inflammable  gas  that  can  be  fur- 
nished with  sufficient  regularity  can  be  used  for  developing 
power.  The  gas  from  coke-ovens  is  a  rich  gas  resembling 
producer-gas  in  its  general  composition.  Natural  gas  consists 
of  90  to  95  per  cent  of  methane  (CH4)  with  a  small  percentage 
of  hydrogen  and  nitrogen  and  traces  of  other  gases.  This  gas 
for  complete  combustion  requires  an  equal  volume  of  oxygen 
and  consequently  about  five  times  its  volume  of  air;  it  is  prob- 
able that  ten  or  twelve  volumes  of  air  can  be  used  to  advantage 
with  this  gas  in  a  gas-engine. 


334 


INTERNAL-COMBUSTION    ENGINES 


Gasoline.  —  The  lighter  distillates  of  petroleum,  known  as  gaso- 
line, are  readily  vaporized  at  atmospheric  pressure,  and  provide 
the  most  ready  means  of  supplying  fuel  to  small  engines ;  engines 
of  several  hundred  horse-power  developed  in  several  cylinders 
have  been  built  for  small  torpedo-boats,  but,  in  general,  the  use 
of  gasoline  has  been  limited  by  its  price  to  comparatively  small 
craft  and  to  automobiles;  in  both  cases,  whether  for  pleasure  or 
for  business,  other  things  than  cost  of  fuel  determine  the  selec- 
tion of  the  engines.  The  same  is  true  for  the  engines  of  rela- 
tively small  power  used  for  stationary  plants. 

The  most  vital  feature  of  the  gasoline-engine  is  the  vaporize^ 
or  carburetor,  and  this  device  has  received  much  attention, 
especially  for  automobile-engines  which  are  run  at  very  high 
speed. 

There  are  three  types  of  carburetors  that  have  been  used  for 
gasoline-engines:  (i)  those  depending  on  direct  vaporization,  (2) 
those  that  depend  on  aspiration  with  a  float,  and  (3)  those 
depending  on  aspiration  without  a  float.  The  earliest  types 
depended  on  direct  vaporization  as  air  was  drawn  through  the 
mass  of  the  fluid,  or  through  or  over  fibrous  material  or  a  sur- 
face of  wire  gauze;  some  of  the  latter  devices  depended  on  such 
a  regulation  of  feed  that  nearly  all  the  fluid  vaporized  as  it  was 
supplied,  leaving  only  a  remnant  to  return  to  the  tank.  But 
in  any  case  there  was  a  chance  of  fractional  vaporization  which 
resulted  in  the  production  of  a  heavier  and  less  tractable 
fluid. 

The  more  recent  carburetors  depend  on  aspiration,  the  air 
supply  being  drawn  past  an  orifice  (or  orifices)  to  which  gaso- 
line is  supplied,  and  from  which  it  can  be  drawn  by  the  air 
more  or  less  in  proportion  as  required.  For  stationary  and 
marine' engines  the  supply  of  gasoline  to  the  aspirator  can  be 
nicely  regulated  by  a  float  which  keeps  a  small  chamber  filled 
just  to  the  level  of  the  aspirating  orifices,  so  that  the  inrush  of 
air  may  draw  out  the  gasoline  in  proper  proportion.  This 
device  has  been  tried  on  automobiles,  but  the  shaking  of  the 
machine  disturbs  the  proper  action  of  the  float. 


KEROSENE    OIL 


335 


A  third  form  of  Carburetor  is  illustrated  by  Fig.  76.  Here 
the  gasoline  is  supplied  by  a  pipe  £  to  a  valve  that  may  be  set 
to  give  good  average  action.  Below  is  a  fine  conical  valve  at 
the  end  of  a  vertical  rod  which  is 
held  up  by  a  light  spring;  at  the 
middle  of  the  spindle  is  a  disk- 
valve  which  fit  sloosely  in  a  sleeve. 
At  aa  are  air-inlet  valves,  and  at 
A  is  the  entrance  to  the  cylinder. 
During  the  suction  or  filling  stroke 
the  spindle  is  drawn  down,  opening 
the  valve  at  the  top  of  the  spindle 
and  allowing  the  air  to  draw 
gasoline  by  aspiration.  Some  of 
the  hot  products  of  combustion 
from  the  exhaust  are  circulated 
around  the  aspirating  chamber  to 
prevent  undue  reduction  of  tem- 
perature. This  type  of  carburetor 
works  well  enough  at  moderate  Fic.76. 

speeds,  but  at  very  high  speeds  the  inertia  of  the  spindle 
and  disk-valve  cannot  be  overcome  rapidly  enough  by  the  air, 
which  is  consequently  throttled,  so  that  there  is  not  the  increase 
of  power  which  might  properly  be  expected  at  such  speeds. 

It  is  alleged  that  this  type  of  vaporizer,  or  carburetor,  can  be 
made  to  deal  with  kerosene  oil  and  alcohol. 

Kerosene  Oil.  —  The  use  of  kerosene  oil  has  been  developed 
to  the  greatest  extent  in  England,  on  account  of  former  restric- 
tions on  the  transportation  and  storage  of  gasoline.  It  has 
been  used  in  America  where  there  is  objection  to  gasoline. 

There  is  much  difficulty  in  vaporizing  or  spraying  kerosene 
oil  so  that  it  can  be  properly  mixed  with  air  at  the  temperature 
for  the  supply  to  an  engine.  On  the  other  hand,  any  attempt 
to  vaporize  the  oil  at  a  high  temperature  results  in  the  deposit 
of  a  hard  graphitic  material. 

One  of  the  most  successful  English  engineers  frankly  accepts 
the  latter  alternative.  The  essential  feature  of  the  carburetor 


OF   THE 
I  lMi\/emcsi*i-\/ 


336  INTERNAL-COMBUSTION    ENGINES 

of  this  engine  is  shown  in  Fig.  77,  which  gives  a  vertical  section 
of  the  cylinder-head  and  of  the  vaporizer;    the    remainder    of 
the    engine   differs  in  no  essential  particular 
from      any      horizontal     gas-engine.       This 
vaporizer,   which   has    a  constricted  neck,  is 
bolted    to    the    cylinder-head;    the    forward 
end    is    jacketed    with  water,  as  is  also  the 
cylinder    of   the    engine;    but  the  after  end, 
FIG  77  which  is  ribbed  internally,  is  not  jacketed;  it 

consequently  remains  at  a  red-heat  when 
the  engine  is  running.  The  oil  for  each  explosion  is  delivered 
into  this  hot  end  of  the  vaporizer,  and  is  vaporized  and  mingles 
with  the  hot  spent  gases;  toward  the  end  of  the  compression 
stroke  the  charge  of  air  which  has  been  drawn  in  and  com- 
pressed enters  the  vaporizer  and  an  explosion  occurs.  When 
the  vaporizer-head  has  become  clogged,  after  24  to  200  hours 
running,  depending  on  the  kind  of  oil  used,  it  is  taken  off  and 
the  hard  adherent  deposit  is  removed;  to  avoid  delay  a  second 
head  is  put  on  for  a  corresponding  run.  This  engine  is 
governed  by  controlling  the  oil  supply;  the  governor  opens  a 
bypass- valve  on  the  oil  supply-pipe  and  allows  a  part  to  return 
to  the  tank.  The  hit-or-miss  principle  is  not  applicable,  as  the 
vaporizer  would  become  too  cool.  Before  starting,  the  vaporizer 
must  be  heated  to  a  dull  red  by  aid  of  a  kerosene  or  gasoline 
torch.  The  engine  can  burn  also  crude  petroleum,  or  an 
unrefined  distillate  resembling  kerosene. 

Alcohol.  —  The  demand  for  gasoline  maintains  the  price  at 
a  point  which  makes  it  possible  in  some  countries  to  use  alcohol, 
if  it  can  be  relieved  from  special  taxation.  To  make  alcohol 
unfit  for  any  but  mechanical  purposes  it  is  mixed  with  a  little 
wood-alcohol  and  benzine;  this  process,  called  denaturizing,  has 
little  if  any  effect  on  its  combustion.  For  combustion  the 
amount  of  water  brought  over  during  distillation  should  be 
limited  to  a  small  percentage.  The  use  of  alcohol  for  power  in  this 
country  has  only  recently  been  made  possible  under  the  internal- 
revenue  laws,  so  that  we  have  no  experience  with  it.  There 


THE    FOUR-CYCLE    ENGINE 


337 


appears  to  be  no  reason  why  there  should  be  trouble  in  the  use 
of  some  form  of  carburetor  like  those  used  for  gasoline  engines. 
The  Four-cycle  Engine.  —  Fig.  78  gives  a  vertical  section  of  a 
Westinghouse  four-cycle  gas-engine  built  in  various  sizes,  up  to  85 
horse-power  with  one  cylinder,  and  up  to  360  with  three  cylinders. 
Massive  engines  of  this  type  are  horizontal  with  double- 
acting  pistons,  having 
two  cylinders  tandem 
or  four  twin-tandem. 
It  is  somewhat  curious 
that  while  massive 
steam-engines  tend  to- 
wards the  upright  con- 
struction, large  gas- 
engines  appear  to  be 
all  horizontal;  it  may 
be  for  the  convenience 
of  the  tandem  arrange- 
ment. In  Fig.  78  the 
frame  of  the  engine  is 
arranged  to  form  an 
inclosed  crank  -  case, 
which  is  somewhat 
unusual  for  gas- 
engines.  The  piston 
is  in  the  form  of  a 


plunger,    so     that     no  FlG  ?8< 

cross-head    is    needed; 

a  common  arrangement  for  all  except  massive  gas-engines. 
The  cylinder  barrel  and  head  are  water- jacketed,  the  inlet 
and  exits  being  at  H  and  K.  Gas  and  air  enter  the  mixer- 
chamber  M  by  separate  pipes  (not  shown)  and  pass  by  N 
to  the  inlet-valve  /;  the  engine  is  controlled  by  a  throttle- valve 
directly  connected  to  a  ball-governor  beneath  the  chamber  M, 
but  omitted  from  the  figure.  The  valve  is  a  piston-valve 
with  separate  air  and  gas  passages,  which  works  in  a  sleeve 


338  INTERNAL-COMBUSTION    ENGINES 

that  can  be  moved  by  hand;  this  sleeve  may  be  set  by  hand 
to  give  any  desired  mixture,  and  the  proportion  of  the  inlet 
areas  for  gas  and  air  having  been  once  set,  the  relative 
areas  remain  unchanged,  while  the  governor  adjusts  the 
piston-valve  to  give  the  amount  of  mixture  that  may  be 
demanded  by  the  load  on  the  engine.  The  inlet-valve  J  and 
the  exhaust-valve  E  are  each  moved  by  cams  at  B  and  at  A  as 
indicated,  the  cams  making  one  revolution  for  each  double 
revolution  of  the  engine  required  for  the  four-stroke  cycle. 
Large  sizes  have  the  exhaust- valve  water-cooled,  to  prevent 
burning  the  valve,  and  to  avoid  danger  of  pre-ignition.  Near  A 
there  is  a  handle  for  shifting  into  action  the  starting-cam  which 
reduces  compression  when  the  engine  is  started.  At  F  are  two 
low-tension  make-and-break  ignitors,  either  of  which  can  be 
thrown  into  action;  they  are  worked  by  cams  on  the  shaft  that 
operates  the  valve  /. 

Two-cycle  Engines.  —  The  two  strokes  of  a  four-cycle  engine 
which  exhaust  the  spent  charge  and  draw  in  the  new  charge  are 
performed  with  a  pressure  in  the  cylinder  only  a  little  higher  or 
lower  than  that  of  the  atmosphere,  and  could  be  omitted  with 
advantage  provided  the  operations  could  be  performed  in  some 
other  way.  The  first  successful  attempt  at  a  two-stroke  cycle 
was  that  by  Dugald  Clerk,  who  made  the  following  changes: 
(i )  he  cut  a  ring  of  exhaust  ports  through  the  cylinder  walls  that 
were  over-run  and  opened  by  the  piston  near  the  end  of  the 
expansion  stroke,  through  which  the  major  part  of  the  spent 
gases  escaped  during  release;  and  (2)  he  provided  a  pump  set 
about  half  a  stroke  ahead  of  the  engine  piston,  which  compressed 
the  new  charge  to  about  ten  pounds  above  the  atmosphere;  as 
soon  as  the  exhaust  had  sufficiently  reduced  the  pressure  in  the 
cylinder,  this  new  charge  opened  the  inlet- valve  and  entered  the 
cylinder,  blowing  the  remainder  of  the  spent  gases  out  through 
the  ports  in  the  cylinder  walls.  The  piston  closed  these  ports 
and  compressed  the  charge  on  the  return  stroke,  so  that  only 
two  strokes  were  required  to  complete  the  cycle,  and  the  engine 
approximated  the  condition  of  a  single-acting  steam-engine  in  its 


TWO-CYCLE    ENGINES  339 

regularity  of  rotative  velocity.  The  engine  could  also  develop 
twice  as  much  power  for  its  size  as  a  four-cycle  engine,  and  in 
certain  tests  by  Mr.  Clerk,  showed  a  slightly  better  economy 
than  the  older  type  of  engine.  But  the  operation  of  replacing 
the  remnants  of  the  spent  charge  by  the  fresh  charge  in  engines 
of  this  type  is  rather  delicate,  there  being  a  chance  that  some  of 
the  spent  charge  will  remain,  or  that  some  of  the  fresh  charge 
will  be  wasted;  it  is  likely  that  the  charges  mingle  and  that  the 
engine  experiences  both  defects.  Eventually  the  Clerk  engine 
was  withdrawn  from  the  market,  but  the  principles  are  used  for 
two  types  of  engines:  (i)  small  gasoline  engines  for  launches  and 
other  small  craft,  and  (2)  large  engines  built  for  burning  blast- 
furnace gas. 

Gasoline-engines  of  small  power  and  moderate  rotative  speed 
have  been  made  on  the  two-cycle  principle  by  enclosing  the 
crank-  and  connecting-rod  in  a  casing,  so  that  the  piston  may  act 
as  the  compressing-pump.  On  the  up-stroke  a  charge  of  air 
and  gasoline  is  drawn  into  the  crank-case,  and  it  is  slightly  com- 
pressed on  the  down-stroke.  There  are  two  sets  of  ports  cut 
through  the  cylinder  walls  near  the  end  of  the  down-stroke  and 
are  opened  by  the  piston;  these  are  on  opposite  sides  of  the 
cylinder;  one  set,  which  is  opened  slightly  earlier  than  the  other, 
forms  the  exhaust-ports  and  the  other  the  inlet-ports  which  are  in 
communication  with  the  crank-case,  and  therefore  supply  air 
and  gasoline  to  replace  the  spent  charge.  A  barrier  is  cast  on 
the  cylinder-head  which  prevents  the  fresh  charge  from  flowing 
directly  across  from  the  inlet  to  the  exhaust,  but  nevertheless  the 
action  is  probably  much  inferior  to  that  of  Clerk's  engine,  which 
had  the  charge  supplied  at  the  cylinder-head.  These  engines  are 
nearly  valveless  and  can  run  in  either  direction,  and  on  account 
of  the  simplicity  and  small  cost  have  found  favor  for  propelling 
small  craft  at  moderate  speeds. 

If  any  attempt  is  made  to  run  two-cycle  engines  at  a  high 
rotative  speed  there  is  difficulty  in  obtaining  proper  exhaust 
and  supply,  since  both  operations  are  performed  under  gaseous 
pressure  that  cannot  well  be  increased.  Recently  two-cycle 


340  INTERNAL-COMBUSTION    ENGINES 

engines  have  been  introduced  on  automobiles  to  a  limited  extent. 
Two  German  engineering  firms  have  developed  two-cycle  engines 
especially  for  burning  blast-furnace  gas  on  a  large  scale,  as  much 
as  1500  horse-power  in  a  single  cylinder. 

The  Korting  engine  (built  by  the  de  la  Verne  Machine 
Company)  is  a  double-acting  engine  which  has  a  piston  nearly 
as  long  as  the  stroke  of  the  engine.  At  the  middle  of  the  length 
of  the  cylinder  is  a  ring  of  exhaust-ports  that  are  uncovered  at 
the  end  of  each  stroke,  and  discharge  burnt  gases  from  first 
one  end  of  the  cylinder  and  then  the  other.  By  the  side  of  the 
engine-cylinder,  and  arranged  in  tandem  so  that  they  can  be 
driven  by  one  crank  (which  has  a  lead  of  uo°),  are  two  pumps, 
one  for  compressing  air,  and  the  other  gas.  The  capacities 
of  the  two  pumps  are  designed  for  the  kind  of  gas  to  be 
burned. 

The  air-pump  compresses  to  eight  pounds  above  the  atmos- 
phere and  delivers  air  to  the  admission  valves,  which  are  lifted  by 
cams  at  the  time  when  the  release  is  completed.  The  governor 
controls  a  bypass-valve  which  puts  the  two  ends  of  the 
pump  in  communication  for  about  half  of  the  discharge 
stroke  of  that  pump,  which  accomplishes  two  purposes.  In 
the  first  place  the  compression  of  the  gas  begins  only  when  the 
bypass-valve  is  closed,  and  consequently  is  to  a  less  pressure 
than  that  of  the  air;  consequently  the  air  backs  up  in  the  gas- 
supply  pipe,  and  when  the  engine  admission  valve  is  opened  it 
supplies  only  air  which  clears  the  cylinder  of  spent  gases;  after- 
ward the  cylinder  receives  its  charge  of  mixed  gas  and  air.  By 
careful  design  and  adjustment  it  is  attempted  to  fill  the  cylinder 
without  wasting  gas  at  the  exhaust-ports,  but  tests  show  an  appre- 
ciable percentage  of  unburned  gas  in  the  exhaust.  And  in  the 
second  place  the  governor  can  regulate  the  closure  of  the  bypass- 
valve  so  as  to  adjust  the  amount  of  gas  to  the  work.  Since  the 
range  of  explosive  mixture  of  blast-furnace  gas  is  not  wide,  this 
method  of  regulation  appears  to  be  adapted  only  to  fairly  uni- 
form loads. 

The  Oechelhauser  gas-engine  has  two  single-acting  pistons  or 


THE    DIESEL    MOTOR 


341 


plungers  in  a  long  open-ended  cylinder;  these  plungers  are 
connected  to  cranks  at  180°  so  that  they  approach  or  recede 
from  the  middle  of  the  cylinder  simultaneously.  The  engine 
has  a  cross-head  at  each  end  of  the  cylinder  to  take  the  cross- 
thrust  of  the  connecting-rod,  so  that  the  engine  extends  to  a 
great  length  on  a  horizontal  foundation.  Toward  the  crank- 
end  of  the  cylinder  there  is  a  ring  of  exhaust-ports  uncovered  by 
the  inner  (or  crank-end)  piston,  and  toward  the  outer  end  of  the 
cylinder  there  is  another  row  uncovered  by  the  outer  piston;  a 
part  of  these  outer  ports  supply  air,  and  a  part  gas.  These  air- 
and  gas-ports  may  be  controlled  by  annular  valves  that  are  set 
by  hand  when  the  engine  uses  blast-furnace  gas.  Under  these 
conditions  the  engine  is  regulated  by  a  governor,  which  controls 
the  pumps  that  supply  air  and  gas.  These  pumps,  which  are 
driven  from  the  outer  cross-head,  have  bypass-valves  which 
connect  the  two  ends  and  begin  to  deliver  only  when  the 
bypass-valves  are  shut  by  the  governor,  so  that  the  charge  is 
adjusted  in  amount  to  the  load.  When  the  engine  uses  a  rich 
gas  that  has  a  wide  explosive  range,  the  governor  controls  the 
annular  valves  at  the  gas-ports  and  varies  the  mixture. 

The  Diesel  Motor.  —  A  new  form  of  internal-combustion 
engine  was  described  by  Rudolf  Diesel  in  1893,  which  does 
away  with  many  of  the  difficulties 
of  gas-  and  oil-engines,  and  which 
at  the  same  time  gives  a  much 
higher  efficiency.  The  essential 
feature  of  his  engine  consists  in 
the  adiabatic  compression  of 
atmospheric  air  to  a  sufficient 
temperature  to  ignite  the  fuel 
which  is  injected  at  a  determined 
rate  during  part  of  the  expansion 
or  working  stroke. 

The  theoretical  cycle  is  shown  by 
Fig.79,which  represents  four  strokes 
of  a  single-acting  piston  or  plun- 


FIG.  70 


342 


INTERNAL-COMBUSTION    ENGINES 


ger.  Atmospheric  air  is  drawn  in  from  a  to  b  and  is  com- 
pressed from  b  to  c  to  a  pressure  of  500  pounds  to  the 
square  inch  and  a  temperature  of  1000°  F.  From  c  to  d  fuel 
is  injected  in  a  finely  divided  form,  and  as  there  is  air  in 
excess  it  burns  completely  at  a  rate  that  can  be  controlled 
by  the  injection  mechanism.  Thus  far  the  only  fuel  used 
is  petroleum  or  some  other  oil.  At  d  the  supply  of  fuel  is 
interrupted,  and  the  remainder  of  the  working  stroke,  de, 
is  an  adiabatic  expansion.  The  cycle  is  completed  by  a  release 
at  e  and  a  rejection  of  the  products  of  combustion  from  b  to  a. 
The  cycle  has  a  resemblance  to  that  of  the  Otto  engine,  but 
differs  in  that  the  air  only  is  compressed  in  the  cylinder  and 
the  combustion  is  accompanied  by  an  expansion.  Diesel,  in 
his  theoretic  discussion  of  his  engine,  stipulates  that  the  rate 
of  combustion  shall  be  so  regulated  that  the  temperature  shall 
not  rise  during  the  injection  of  fuel,  and  that  the  line  cd  shall 
therefore  be  very  nearly  an  isothermal  for  a  perfect  gas.  Since 
the  fuel  is  added  during  the  operation  represented  by  the  line 
cdj  the  weight  of  the  material  in  the  cylinder  increases  and  its 
physical  properties  change,  so  that  the  line  will  not  be  a  true 
isothermal.  The  fact  that  there  is  air  in  excess  makes  it  prob- 


FIG.  80 


able  that  these  changes  of  weight  and  properties  will  be  insig- 
nificant. On  the  other  hand,  it  is  not  probable  that  in  practice 
the  rate  of  injection  of  fuel  will  be  regulated  so  as  to  give  no 


THE    DIESEL   MOTOR  343 

rise  of  temperature,  or  that  there  is  any  great  advantage  in  such 
a  regulation  if  the  temperature  is  not  allowed  to  rise  too  high. 

The  diagram  from  an  engine  of  this  type  is  shown  by  Fig.  80, 
which  appears  to  show  an  introduction  of  fuel  for  one-eighth 
or  one-seventh  of  the  working  stroke.  It  is  probable  that  the 
compression  and  the  expansion  (after  the  cessation  of  the  fuel 
supply)  are  not  really  adiabatic,  though  as  there  is  nothing  but 
dry  gas  in  the  cylinder  during  those  operations  the  deviation 
may  not  be  large.  The  sides  and  heads  of  the  cylinders  of  all 
the  engines  thus  far  constructed  are  water-jacketed,  though 
the  use  of  such  a  water-jacket  and  the  consequent  waste  of  heat 
was  one  of  the  difficulties  in  the  use  of  internal-combustion 
engines  that  Diesel  sought  to  avoid  by  controlling  the  rate  of 
combustion.  The  statement  on  page  39  that  the  maximum 
efficiency  is  attained  by  adding  heat  only  at  the  highest  tem- 
perature has  no  application  in  this  case.  The  real  conditions 
are  that  heat  cannot  at  first  be  added  at  a  temperature  higher 
than  that  due  to  compression  (about  1000°  F.),  but  as  combus- 
tion proceeds  heat  can  be  added  at  higher  temperature  and 
with  greater  efficiency.  The  fuel  may  be  regulated  so  as  to 
avoid  temperatures  at  which  dissociation  has  an  influence  and 
after-burning  can  be  avoided. 

The  oil  used  as  fuel  is  injected  in  form  of  a  spray  by  air  that 
is  compressed  separately  in  a  small  pump  to  30  or  40  pounds 
pressure  above  that  in  the  main  cylinder;  of  course  it  is  neces- 
sary to  cool  this  portion  of  the  air  after  compression  to  avoid 
premature  ignition.  The  engines  that  have  been  used  are 
described  as  giving  a  clear  and  nearly  dry  exhaust.  In  damp 
weather  the  exhaust  shows  a  little  moisture,  probably  from  the 
combustion  of  hydrogen  in  the  oil.  The  cylinder  when  opened 
shows  a  slight  deposit  of  soot  on  the  head.  It  appears  there- 
fore that  Diesel  has  succeeded  in  constructing  an  engine  for 
burning  heavy  oils  with  good  economy  and  without  the  annoy- 
ances of  an  igniting  device.  The  engines  have  the  further 
advantage  in  that  the  work  can  be  regulated  by  the  amount 
of  fuel  supplied,  which  amount  is  not  controlled,  as  in  explosive 


244  INTERNAL-COMBUSTION    ENGINES 

engines,  by  the  necessity  to  form  an  explosive  mixture.  The 
discussion  of  the  theoretical  efficiency  of  the  cycle  shows  that 
the  efficiency  increases  as  the  time  of  injection  of  fuel  is  shortened. 
In  practice  the  engine  shows  a  slight  decrease  in  economy  for 
light  loads,  due  probably  to  the  losses  by  radiation  and  to  the 
water-jacket,  which  are  nearly  constant  for  all  loads. 

In  the  exposition  of  the  theory  of  his  motor,  Diesel  *  claims 
that  all  kinds  of  fuel,  solid,  liquid,  and  gaseous,  can  be  burned 
in  his  motor.  As  yet  oil  only  has  been  used ;  the  choice  of  petro- 
leum or  other  heavy  oil  has  probably  been  due  to  the  low  cost 
of  such  oils.  It  is  evident  that  gas  may  be  used  in  this  type 
of  engine;  the  gas  can  be  compressed  separately  to  a  pressure 
somewhat  higher  than  that  in  the  main  cylinder,  much  as  the 
air  is  which  is  used  for  injecting  oil.  It  does  not  appear  neces- 
sary to  cool  the  gas  after  compression,  as  it  will  burn  only  when 
supplied  with  air. 

There  appears  to  be  no  insurmountable  difficulty  in  supply- 
ing powdered  solid  fuel  to  this  engine.  The  presence  of  the 
ash  from  such  fuel  in  the  cylinder  may,  however,  be  expected 
to  give  trouble.  Diesel  claims  that  with  a  large  excess  of  air 
(for  example,  a  hundred  pounds  of  air  for  one  pound  of  coal) 
the  ash  will  be  swept  out  of  the  cylinder  with  the  spent  gases 
and  will  not  give  trouble;  but  that  claim  has  not  as  yet  been 
substantiated. 

Diesel's  original  discussion  of  his  motor  contemplated  a  com- 
pound compressing-pump,  one  stage  to  give  isothermal  compres- 
sion, and  the  second  stage  to  give  adiabatic  compression;  also  a 
compound  motor,  the  first  cylinder  having  isothermal  expansion 
with  a  supply  of  fuel,  and  the  second  cylinder  an  adiabatic  ex- 
pansion. He  gives  with  that  discussion  a  theoretical  diagram 
approaching  Carnot's  cycle  in  appearance  and  efficiency.  If 
this  variety  of  the  motor  were  mechanically  practicable  it  Would 
have  the  defects  of  Carnot's  cycle  for  gas,  namely,  the  diagram 
would  be  very  long  and  attenuated,  and  even  with  the  very  high 
pressures  contemplated  would  give  a  relatively  small  power. 

*  Rational  Heat  Motor;  Rudolf  Diesel,  trans.     Bryan  Donkin. 


THE    DIESEL   MOTOR  345 

A  theoretical  discussion  of  the  efficiency  of  the  cycle  for  the 
simple  engine  as  represented  by  Fig.  79  may  be  obtained  by 
considering  that  heat  is  added  at  constant  temperature  from  c 
to  d  and  that  heat  is  rejected  at  constant  volume  from  e  to  b, 
bearing  in  mind  that  be  and  dc  represent  adiabatic  changes. 

From  equation  (75),  page  63,  the  expression  for  the  heat 
supplied  from  c  to  d  is,  for  one  pound  of  working  substance, 


The  heat  rejected  at  constant  volume  is 

Qt  =  c,  (T,  -  Ti)  -  *  (71.  -  7\). 

rC 

Since  the  expansion  de  is  adiabatic, 


T         T  T 

Te==Td(vJ        'T'(v 

but  since  the  compression  be  is  also  adiabatic, 

T         T    f 
Tc  =    T* 

and  consequently 


for  ve  =  vb.     Replacing  Te  by  its  value  in  the  expression  for 
Q2,  we  have 


Finally,  the  efficiency  appears  to  be 

c  T 


.  (I88) 

-11 

Inspection   of  the   equation   shows   that   the   efficiency    may 
be  increased  by  raising  the  temperature  Te  or  by  reducing  the 


346  INTERNAI^COMBUSTION    ENGINES 

temperature  Tb.  The  latter  is  practically  the  temperature  of 
the  atmosphere,  but  Tc  may  be  made  any  desired  temperature 
by  reducing  the  clearance  of  the  cylinder  and  thus  raising  the 
pressure  at  the  end  of  compression.  Again,  the  efficiency 
may  be  increased  by  reducing  the  time  during  which  fuel  is 
injected,  that  is,  by  reducing  the  ratio  vd  :  ve,  as  may  be  proved 
by  a  series  of  calculations  with  different  values  for  that  ratio. 
This  is  a  very  important  conclusion,  as  it  shows  that  the  engine 
will  have  in  practice  little  if  any  falling  off  in  efficiency  at  reduced 
loads. 

It  is  reported  that  a  clearance  of  something  less  than  7  per 
cent  is  associated  with  a  compression  to  500  pounds  and  a 
temperature  of  1000°  F.,  or  more.  Taking  the  pressure  of 
the  atmosphere  at  14.7  pounds  per  square  inch,  adiabatic  com- 
pression to  500  pounds  above  the  atmosphere  or  to  514.7  pounds 
absolute  requires  a  clearance  of 


so  that  the  clearance  is 

0.0796  -s-  fi  —  0.079}  =  0-0865 

of  the  piston  displacement. 

If  the  temperature  of  the  atmosphere  be  taken  at  70°  F. 
or  530  absolute,  the  temperature  after  adiabatic  compression 
becomes 


absolute,  or  1020°  F. 

If  it  be  further  assumed  that  fuel  is  supplied  for  one- tenth 
of  the  working  stroke,  then 

vd  =  o.i  (vb  -  va)  4-  va  =  [o.i  (i  —  0.0796)  +  0.0796]  vb 

=  0.1716  vb. 


ENGINES   FOR   SPECIAL   PURPOSES  347 

The  equation  for  efficiency  gives  in  this  case 


0.58. 

1.405  X  53.22  X  1480  loge    '1 

0.0790 

Engines  for  Special  Purposes.  —  Small  engines  can  be  made 
to  give  any  required  degree  of  regularity  for  electrical  or  other 
purposes,  by  giving  a  sufficient  weight  to  the  fly-wheel;  for 
large  power  the  same  object  can  be  attained  by  using  a  number 
of  cylinders,  by  making  the  engine  double  acting,  by  the  con- 
struction of  two-cycle  engines,  or  by  the  combination  of  two  or 
more  of  these  devices. 

The  four-cycle  engine  has  not  as  yet  been  made  reversible, 
and  even  if  the  complexity  of  valve-gear  for  running  in  both 
directions  could  be  accepted,  it  appears  likely  that  a  special 
starting  device  would  be  required  for  every  reversal.  Reversing 
launches  and  automobiles  is  done  by  aid  of  a  mechanical  revers- 
ing gear,  except  that  for  some  small  boats  a  reversing  propeller 
is  used.  Such  gear  for  large  ships  appears  to  be  dangerous  as 
well  as  impracticable. 

Two-cycle  engines  would  not  require  much  complication  of 
valve-gear  to  make  them  reversible,  and  would  have  some 
advantage  on  account  of  the  greater  frequency  of  working 
strokes;  they  also  might  require  the  use  of  a  starting  gear 
for  every  reversal.  Small  launches  with  two-cycle  engines 
are  readily  reversed  by  hand,  but  such  small  craft  can  be 
fended  off,  and  a  failure  to  reverse  need  not  be  serious. 

The  engine  with  separate  compressing-pump  discussed  on 
page  305,  appears  to  show  greater  promise  for  marine  or  other 
purposes  where  ready  reversal  is  essential.  Even  with  the 
pump  geared  directly  to  the  engine,  it  was  found  possible  to 
reverse  a  two-cylinder  engine  promptly  with  a  valve-gear  but 
little  more  complicated  than  that  for  a  steam-engine.  But  for 
marine  purposes  the  engines  could  be  placed  in  two  groups  ;  one 


248  INTERNAI^COMBUSTION    ENGINES 

group  could  be  connected  to  the  propeller  shaft  (or  shafts)  and 
worked  without  compressor-pumps,  and  the  other  group  at  any 
convenient  place  could  drive  the  compressor-pumps  for  the 
whole  system.  Such  an  arrangement  should  give  practically 
the  same  certainty  of  maneuvering  as  steam-engines. 

The  application  of  gas-engines  to  large  ships  cannot  be 
considered  to  be  accomplished  till  producers  have  been  made 
that  can  use  all  grades  of  bituminous  coal,  including  inferior 
qualities. 

Automobiles  are  commonly  driven  by  four-cycle  gasoline 
engines,  and  have  a  rather  formidable  array  of  mechanical 
devices,  including  clutches  to  release  the  engine  for  starting,  or 
when  the  carriage  is  standing  still,  several  change-speed  gears 
for  running  slowly  and  climbing  hills,  and  a  reversing  mechanism. 
All  of  this  entails  weight,  cost  and  depreciation,  and  while  gaso- 
line vehicles  can  be  handled  efficiently  by  skilled  drivers  they  have 
not  the  facility  of  control  that  is  readily  given  to  steam-carriages. 
The  speed  and  power  can  be  controlled  by  throttling  the  charge 
and  by  delaying  the  ignition;  the  mixture  may  be  included  in 
the  methods  of  control,  but  probably  it  is  better  left  alone  when 
well  adjusted. 

Economy  of  Gas-Engines.  —  It  will  be  convenient  to  consider 
the  economy  of  gas-engines  before  discussing  the  economy  of 
engines  using  special  fuel  like  gasoline  or  oil,  because  it  is  only 
this  class  of  engines  that  can,  by  association  with  the  gas-producer, 
make  use  of  all  kinds  of  fuel,  and  especially  of  coal. 

It  will  be  convenient  also  to  make  such  inquiry  as  may  be 
possible  concerning  the  influence  of  various  conditions  on  the 
economy  of  gas-engines  before  trying  to  determine  what  economy 
may  properly  be  attributed  to  them. 

There  are  five  conditions  that  can  be  enumerated  which  have 
an  effect  on  the  efficiency  of  gas-engines: 

(1)  Compression. 

(2)  Mixture. 

(3)  Size. 

(4)  Quality  of  gas. 


ECONOMY    OF   GAS-ENGINES  349 

(5)  Time  of  ignition. 

(1)  The  influence  of  compression  is  indicated  theoretically  by 
equation  (187),  page  312,  which  shows  that  the  efficiency  may  be 
expected  to  increase  progressively  with  increasing  compression. 
To  exhibit  this  feature  and  to  compare  it  with  the  results  obtained 
in  practice,  the  following  table  has  been  computed  for  tests  2,  5, 
and  7  of  Table  XXXV,  page  350.     The  composition  of  the  illumin- 
ating-gas used  was  similar  to   that   on   page  315;  the  original 
detailed  report  of  these  tests  shows  little  variation  in  composition. 

Number  of  tests   ...      2               5  7 

Ratio  of  compression     .4.98  4-59  3-84 

Theoretical  efficiency      .  0.479  0.461  0.420 

Thermal  efficiency      .     .0.270  0.264  0.252 

Ratio 0.564  0.573  0.600 

Such  a  comparison  is  commonly  considered  to  show  that  the 
actual  efficiency  follows  the  theoretical  efficiency,  the  former 
being  based  on  the  indicated  horse-power,  and  being  obtained 
by  dividing  42.42  (the  equivalent  of  one  horse-power  in  thermal 
units  per  minute)  by  the  thermal  units  per  indicated  horse-power 
per  minute.  But  if  the  brake  horse-power  is  taken  as  the  basis 
of  comparison,  as  has  already  been  shown  to  be  proper,  there 
appears  to  be  practically  no  advantage  in  the  higher  compression 
for  the  illuminating-gas;  for  the  power-gas  there  is  no  advantage 
in  a  compression  beyond  four  and  a  half.  There  is,  however, 
an  advantage  in  that  a  higher  compression  gives  a  larger  mean 
effective  pressure  and  greater  power. 

(2)  A  stronger  mixture  of  gas  and  air  may  in  general  be 
expected  to  yield  more  work  than  a  weaker  one,  as  is  shown  by 
comparing  the  trios  of  tests  with  the  same  compression  both  for 
illuminating-gas  and  for  power-gas;  but  there  is  usually  some 
mixture  that  will  give  the  best  economy.     This  mixture  should 
be  selected  from  a  proper  series  of  engine-tests  rather  than  by 
some  other  method,  but  as  this  involves  a  large  amount  of  exper- 
imental work,  a  satisfactory  discussion  of  this  feature  is  not 
always  possible.     The  tests  in  Table  XXXV  show  that  for  both 


350 


INTERNAL-COMBUSTION    ENGINES 


kinds  of  gas  the  richest  mixture  used  is  the  most  economical, 
basing  the  comparison  on  brake  horse-power  as  should  be  done. 
The  first  trio  of  tests  shows  a  distinct  minimum  for  a  ratio  of  ten 

TABLE    XXXV. 

GAS-ENGINE    WITH  ILLUMINATING-  AND  WITH    POWER-GAS. 

DIAMETER    8.6    INCHES;     STROKE     13     INCHES. 

PROFESSOR  MEYER,  Mitteilungen  uber  Forschungsarbeiten  Heft  8,  1903,, 


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to  one;  the  minimum  per  brake  horse-power  will  be  found  for  a 
richer  mixture,  on  account  of  the  better  mechanical  efficiency 
which  accompanies  the  larger  power  which  such  a  mixture  will 
develop;  it  cannot  be  far  wrong  to  assume  that  the  mixture  of 


ECONOMY   OF  GAS-ENGINES  351 

eight  to  one  will  give  the  minimum  per  brake  horse-power.  The 
remainder  of  the  table  is  less  conclusive,  but  it  appears  likely 
that  a  ratio  of  one  volume  of  illuminating-gas  to  eight  volumes 
of  air  is  proper,  and  that  for  power-gas  the  ratio  should  be  some- 
what larger  than  unity. 

(3)  A  committee  of  the  Institution  of  Civil  Engineers  *  tested 
three  gas-engines  of  varying  size,  but  all  having  the  same  ratio 
of   compression,  and  tested  under  the  same  conditions.     The 
results  that  bear  on  the  question  of  size  are  as  follows : 

Brake  horse-power 5.2     20.9     52.7 

Thermal  units  per  horse-power  per 
minute 

It  is  to  be  remarked  that  the  results  just  quoted  are  remarkably 
low,  but  that  the  composition  of  the  committee  and  the  precau- 
tions taken,  place  them  beyond  cavil.  It  is  somewhat  difficult  to 
account  for  the  difference  between  the  results  just  quoted,  and 
those  given  in  Table  XXXV,  though  part  of  it  is  due  to  the  better 
mechanical  efficiency  of  the  former.  This  was  estimated  to  be 
about  0.87,  while  that  of  the  engine  tested  by  Professor  Meyer 
was  about  0.72;  allowance  for  this  difference  may  be  estimated 
to  reduce  the  results  of  the  first  test  in  Table  XXXV  to  184 
thermal  units  per  brake  horse-power  per  minute.  This  illus- 
trates an  inconvenience  of  using  the  brake  horse-power  as  the 
basis  of  comparison  of  tests  on  different  engines,  since  it  makes 
the  results  depend  on  the  mechanical  condition  of  the  engine; 
however,  this  condition  is  one  of  the  elements  of  practical 
economy. 

(4)  It  is  likely  that  an  engine  will  show  a  better  heat  economy 
when  using  a  richer  gas,  as  is  indicated  by  comparing  the  results 
in  Table  XXXV  with  illuminating-gas  and  with  power-gas;  but 
there  is  not  sufficient  information  to  make  this  feature  decisive. 

(5)  It  is  customary  to  time  the  ignition  so  that  the  maximum 
pressure  shall  come  early  in  the  stroke,  and  that  is  probably 
conducive  to  good  economy;  delaying  ignition,  as  is  done  on 
automobiles  to  reduce  the  power,  is  known  to  be  very  wasteful. 

*  Proc.  Inst.  Civ.  Engrs.,  vol.  clxii,  p.  241. 


352  INTERNAL-COMBUSTION    ENGINES 

Professor  Meyer  made  some  subsidiary  tests  to  determine 
the  influence  of  the  time  of  ignition  on  illuminating-gas  with  the 
results  following: 

Lead  of  ignition,  1.2       5.6      9.7    n.o    10.9     14.2   20.7 

Thermal  units  per  indi- 
cated horse-power  per      216     217     223     216     221     226     260 
minute 

This  appears  to  show  that  any  lead  up  to  15°  would  give  about 
the  same  result  for  this  engine,  but  that  a  greater  lead  was 
undesirable. 

The  question  as  to  the  economy  to  be  expected  from  gas- 
engines  has  been  considered  incidentally  in  our  review  of  the 
influence  of  various  conditions  on  the  economy  of  gas-engines. 
The  best  result  that  is  quoted  is  for  an  engine  tested  by  the 
committee  of  the  Institution  of  Civil  Engineers,  which  used  143 
thermal  units  per  horse-power  per  minute,  when  developing  52.7 
brake  horse-power.  The  gas  used  had  the  composition  by 
volume : 

Hydrocarbons       ...  4.74  Carbon  dioxide      .    .       2.62 

Methane  CH4      .    .    .  33.73  Oxygen 0.27 

Hydrogen       41.29  Nitrogen    .    .    .    .    .      10.22 

Carbon  monoxide    .    .  7.13  Total 100 

Its  heat  of  combustion  determined  by  aid  of  a  Junker  calori- 
meter was  561  B.T.U. 

The  test  of  a  producer  gas-power  plant  at  St.  Louis  given  on 
page  354  used  198  thermal  units  per  brake  horse-power  per 
minute. 

An  engine  developing  728  metric  horse-power  at  Seraing  at 
93  revolutions  per  minute,  used  163  thermal  units  per  brake 
horse-power  per  minute;  the  mechanical  efficiency  being  0.82. 
when  tested  by  Hubert.* 

A  Producer- Gas  Plant.  —  At  the  Louisiana  Purchase  Exposi- 
tion at  St.  Louis  in  1904,  an  extensive  investigation  was  made  oi 
various  fuels  from  all  parts  of  the  United  States,  including  the 

*  Bui.  Soc.  de  I'Industrie  Mineral,  30!  series,  vol.  xiv,  p.  1461. 


A    PRODUCER-GAS    PLANT  353 

development  of  power  by  the  combination  of  a  Taylor  gas-pro- 
ducer with  necessary  adjuncts,  and  a  three-cylinder  Westinghouse 
gas-engine;  a  detailed  report  of  the  tests  is  given  by  Messrs. 
Parker,  Holmes,  and  Campbell,*  the  committee  in  charge. 

The  gas-producer  had  a  diameter  of  7  feet  inside  the  brick 
lining,  and  at  the  bottom  was  a  revolving  ash  table  5  feet  in 
diameter;  the  blast  was  furnished  by  a  steam-blower  supplied 
from  a  battery  of  boilers  used  for  other  purposes;  tests  were 
made  to  determine  the  probable  amount  of  steam  taken  by  the 
blower,  but  the  variation  of  steam-pressure  acting  at  the  blower 
during  tests  made  this  determination  somewhat  unsatisfactory. 
The  cost  of  the  steam  in  coal  of  the  kind  used  for  any  test  could 
be  estimated  closely  from  boiler-tests  made  with  the  same  coal. 

The  gas  from  the  producer  passed  through  a  coke-scrubber, 
and  then  through  a  centrifugal  tar-extractor  using  a  liberal 
amount  of  water.  From  the  extractor  the  gas  passed  through 
a  purifier  filled  with  iron  shavings  to  extract  sulphur.  On  the 
way  to  the  engine  the  gas  was  measured  in  a  meter. 

The  engine-cylinders  were  19  inches  in  diameter  and  had  22 
inches  stroke.  At  200  revolutions  the  engine  was  rated  at  235 
brake  horse-power.  The  engine  was  belted  to  a  direct-current 
generator,  and  the  energy  was  absorbed  by  a  water-rheostat. 

The  results  of  a  test  on  a  bituminous  coal  from  West  Virginia 
have  been  selected  for  presentation.  The  composition  of  the 
coal  by  weight  and  the  gas  by  volume  are: 

Coal.  Gas. 

Moisture   ......       2.22       Carbon  dioxide    ...  8.90 

Volatile  matter     .    .    .     31.05       Carbon  monoxide   .    .  14.77 

Fixed  carbon   ....     59.83       Oxygen      ......  .33 

Ash    ........       6.90       Hydrogen      .....  9.52 

Methane    ......  6.65 

'«"4  Nitrogen   ......     50.83 


Thermal  units  per  ) 
cu.  ft.    (62°  F.,  y  160.5 
14.7  pounds)      ) 

*   U.  S.  Geological  Survey,  Professional  Paper  No.  48. 


354  INTERNAI^COMBUSTION    ENGINES 

TEST  ON  PRODUCER  AND  ENGINE. 

Duration,  hours 24 

Total  coal  fired  in  producer,  pounds 6,000 

Coal  equivalent  of  steam  used  by  blower,  pounds 835 

Coal  equivalent  of  power  to  drive  auxiliary  machinery 299 

Total  equivalent  coal 7>i34 

Thermal  value  of  total,  equivalent  coal,  B.T.U 101,500,000 

Total  gas  (at  62°  F.  and  14.7  pounds),  cu.  ft 415,660 

Thermal  value  of  total  gas      66,700,000 

Efficiency  of  producer o .  65  7 

Electrical  horse-power 199 . 3 

Mechanical  efficiency,  estimated o .  85 

Brake  horse-power 234 

Gas  per  horse-power  per  hour,  cubic  feet      74 .  i 

Thermal  units  per  horse-power  per  minute 198 

Thermal  efficiency  of  brake-power 0.214 

Coal  per  brake  horse-power  per  hour 1.27 

Combined  thermal  efficiency  of  producer  and  engine 0.14 

It  is  interesting  to  compare  these  results  of  a  test  on  a  producer- 
plant  with  the  tests  at  the  pumping-station  at  Chestnut  Hill 
from  which  the  results  quoted  on  page  239  were  taken. 

TEST  AT  CHESTNUT  HILL  PUMPING  STATION. 

Duration  hours, 24 

Coal  required  by  plant,  corrected 16,269 

Thermal  value  of  George's  Creek  coal,  estimated 14,500 

Heat  abstracted  from  one  pound  of  coal  by  boiler 10,690 

Efficiency  of  boiler o .  74 

Indicated  horse-power,  engine 576 

Indicated  horse-power,  pump 530 

Mechanical  efficiency o .  920 

Thermal  units  per  pump  horse-power  per  minute 222 

Thermal  efficiency  pump-power      *  0.191 

Combined  thermal  efficiency  pump  and  boiler 0.14 

Coal  per  pump  horse-power  per  hour 1.21 

If  allowance  is  made  for  the  higher  thermal  value  of  George's 
Creek  coal,  the  coal  consumptions  are  very  nearly  equivalent. 

A  test  on  a  Dowson  suction  producer  by  Mr.  M.  A.  Adam  * 
gave  an  efficiency  of  0.80  to  0.84  after  the  producer  was  well 
started.  If  the  thermal  efficiency  of  an  engine  using  the  gas 
may  be  estimated  from  0.20  to  0.24,  the  combined  efficiency  may 
be  estimated  from  0.16  to  0.20,  which  for  anthracite  coal  would 

*  Proc.  Inst.  Civ.  Engrs.,  vol.  clviii,  p.  320. 


ECONOMY    OF   A    DIESEL   MOTOR  355 

correspond  to  one  pound  per  brake  horse-power  per  hour,  or  0.9 
of  a  pound  per  indicated  horse- power;  the  makers  of  producer 
power-plants  are  now  ready  to  guarantee  a  consumption  of 
one  pound  of  anthracite  per  brake  horse-power  per  hour. 

Economy  of  Oil- Engine.  —  An  engine  of  the  type  described  on 
page  335  was  tested  by  Messrs.  A.  E.  Russell  and  G.  S.  Tower  * 
of  the  Massachusetts  Institute  of  Technology.  The  engine 
had  a  diameter  of  11.22  inches  and  a  stroke  of  15  inches,  and  at 
220  revolutions  per  minute  developed  ten  brake  horse-power; 
the  mechanical  efficiency  was  about  0.72,  so  that  the  indicated 
power  was  about  14;  the  clearance  or  charging  space  was  about 
0.44  of  the  piston  displacement. 

With  kerosene  the  best  economy  was  1.5  pounds  per  brake 
horse-power  per  hour;  this  kerosene  weighed  6.52  pounds 
per  gallon,  flashed  at  104°  F.,  and  had  a  calorific  power  of 
17,222  thermal  units  per  pound. 

The  engine  was  also  tested  with  a  crude  distillate  which 
comes  from  petroleum  after  the  kerosene,  weighing  6.66  pounds 
per  gallon,  with  a  flash-point  at  148°  F.,  and  having  a  calorific 
power  of  19,410  thermal  units  per  pound;  of  this  oil  the  engine 
used  1.3  pounds  per  brake  horse-power  per  hour. 

The  thermal  units  per  horse-power  per  minute  were  430  for 
kerosene  and  420  for  the  distillate;  the  thermal  efficiencies  corre- 
sponding are  0.099  and  o.n  on  the  basis  of  brake  horse-power. 

Economy  of  a  Diesel  Motor.  —  A  70  horse-power  Dies-el 
motor  using  Russian  petroleum,  which  had  a  calorific  power  of 
18,450  thermal  units  per  pound,  was  tested  by  Professor  Meyer  f 
in  1904.  The  diameter  of  the  cylinder  was  15.75  inches,  the 
stroke  was  23.7  inches,  and  the"  ratio  of  compression  was  15.4. 
The  air-pump  had  a  diameter  of  2.2  inches  and  a  stroke  of  5.5 
inches.  At  the  normal  load  of  69.63  metric  horse-power  by  the 
brake  (68.6  English  horse-power)  the  oil-consumption  was  0.429 
pound  per  horse-power  per  hour,  or  132  thermal  units  per  brake 
horse-power  per  minute.  The  thermal  efficiency  was  conse- 

*  Thesis,  M.  I  .T.  1905. 

t  Mitteilungen  iiber  Forschungsarbeiten  Heft  17,  p.  35. 


356 


INTERNAL-COMBUSTION    ENGINES 


quently  0.32.  At  an  overload  amounting  to  85.7  brake  horse- 
power, the  oil-consumption  was  0.42  pound,  and  at  half  load 
(34.4  horse-power)  the  consumption  was  0.50  of  a  pound. 

Since  oil  for  lubrication  of  the  cylinder  is  liable  to  be  burned 
together  with  the  fuel,  it  is  specially  necessary  in  tests  of  engines 
of  this  type  that  error  from  the  effect  of  excessive  use  of  lubri- 
cating-oil  is  to  be  guarded  against. 

Distribution  of  Heat.  —  A  very  interesting  and  instructive 
matter  in  the  discussion  of  tests  on  gas-engines  is  the  distribution 
of  the  heat,  and  especially  of  the  heat  that  is  not  changed  into 
work.  It  cannot  be  considered  that  all  of  this  lost  heat  is  wasted, 
because  any  heat-engine  must  reject  heat,  and  that  for  the  theo- 
retical cycles,  which  are  the  limits  for  practical  engines,  the 
major  part  of  the  heat  is  unavoidably  rejected. 

The  following  table  is  taken  from  a  lecture  by  Mr.  Dugald 
Clerk* 


Distribution  of  Heat. 

Dimension 

of  Engine. 

Work. 

Jacket. 

Exhaust. 

6-75  X  13-7 

o.  16 

0.5I 

0.31 

9.5     X  18.0 

0.22 

26  X  36  ) 

2  cyls.    ) 

0.28 

0-43 
0.24 

o-35 
o-39 

51.2  X  55.13 

0.28 

0.52 

O.20 

The  first  three  show,  together  with  a  notable  gain  in  efficiency, 
a  strong  tendency  to  shift  the  waste  heat  from  the  water-jacket 
to  the  exhaust,  as  the  engine  increases  in  size;  the  last  test  is 
from  an  engine  using  blast-furnace  gas,  and  which  is  liberally 
cooled  with  water.  The  whole  table,  and  especially  the  last 
two  examples,  show  that  to  a  large  extent  an  engineer  may  decide 
in  the  design  of  an  engine,  whether  he  will  withdraw  heat  by 
thorough  cooling,  or  allow  the  heat  to  be  suppressed  by  disso- 
ciation and  thrown  out  in  the  exhaust. 

Mean  Effective  Pressure.  —  In  the  design  of  a  gas-engine  the 

*  Forest  Lecture.     Inst.  Civ.  Eng.  cxliii.  p.  21. 


WASTE-HEAT    ENGINES  357 

first  question  to  be  determined  is  the  mean  effective  pressure 
that  is  desired  or  can  be  obtained.  This  must  depend  on  the 
fuel  and  its  mixture  with  air,  and  on  the  degree  of  compression. 
There  does  not  at  the  present  time  appear  to  be  information 
that  will  serve  as  the  basis  of  a  working  theory  for  determining 
the  mean  effective  pressure  even  when  these  features  are 
determined. 

It  is  desirable,  in  order  that  the  engine  shall  be  powerful  and 
compact,  that  the  mean  effective  pressure  shall  be  high;  English 
engineers  commonly  make  use  of  90  to  100  pounds  mean  effective 
pressure;  but  German  engineers  who  have  had  experience  with 
very  large  engines  for  which  pre-ignition  is  dangerous,  have  been 
content  with  60  pounds  or  less. 

Waste- heat  Engines.  —  On  page  180  attention  was  called  to 
the  fact  that  the  exhaust-steam  from  a  steam-engine  could  be 
used  for  vaporizing  some  fluid  like  sulphur  dioxide,  and  that 
thereby  the  temperature  range  could  be  extended.  The  only 
tests  quoted  failed  to  show  the  advantage  that  might  be  expected 
when  this  method  is  used  with  steam-engines.  But  the  exhaust 
from  a  gas-engine  is  very  hot,  probably  1000°  F.,  or  over,  and 
there  appears  to  be  no  reason  why  the  heat  should  be  wasted, 
as  it  could  readily  be  used  to  form  steam  in  a  boiler  or  for  other 
purposes. 


CHAPTER    XV. 

COMPRESSED    AIR. 

COMPRESSED  air  is  used  for  transmitting  power,  for  storing 
energy,  and  for  producing  refrigeration.  Air  at  moderate 
pressure,  produced  by  blowing-engines,  is  used  in  the  production 
of  iron  and  steel;  and  currents  of  air  at  slightly  higher  pressure 
than  that  of  the  atmosphere  (produced  by  centrifugal  fan- 
blowers)  are  used  to  ventilate  mines,  buildings,  and  ships,  and 
for  producing  forced  draught  for  steam-boilers.  Attention  will 
be  given  mainly  to  the  transmission  and  storage  of  energy.  The 
production  and  use  of  ventilating  currents  require  and  are  sus- 
ceptible of  but  little  theoretical  treatment.  Refrigeration  will 
be  reserved  for  another  chapter. 

A  treatment  of  the  transmission  of  power  by  compressed  air 
involves  the  discussion  of  air-compressors,  of  the  flow  of  air 
through  pipes,  and  of  compressed-air  engines  or  motors.  The 
storage  of  energy  differs  from  the  transmission  of  power  in  that 
the  compressed  air,  which  is  forced  into  a  reservoir  at  high 
pressure,  is  used  at  a  much  lower  pressure  at  the  air-motor. 

Air-Compressors.  —  There  are  three  types  of  machines  used 
for  compressing  or  moving  air:  (i)  piston  air-compressors,  (2) 
rotary  blowers,  (3)  centrifugal  blowers  or  fans. 

The  piston  air-compressor  is  always  used  for  producing  high 
pressures.  It  consists  of  a  piston  moving  in  a  cylinder  with 
inlet-  and  exit-valves  at  each  end.  Commonly  the  valves  are 
actuated  by  the  air  itself,  but  some  compressors  have  their  valves 
moved  mechanically.  Blowing-engines  are  usually  piston- 
compressors,  though  the  pressures  produced  are  only  ten  or 
twenty  pounds  per  square  inch. 

Rotary  blowers  have  one  or  more  rotating  parts,  so  arranged 
that  as  they  rotate,  chambers  of  varying  capacity  are  formed, 

358 


FLUID    PISTON-COMPRESSORS  359 

which  receive  air  at  atmospheric  pressure,  compress  it,  and 
deliver  it  against  a  higher  pressure.  They  are  simple  and  com- 
pact, but  are  wasteful  of  power  on  account  of  friction  and  leakage, 
and  are  used  only  for  moderate  pressures. 

Fan-blowers  consist  of  a  number  of  radial  plates  or  vanes, 
fixed  to  a  horizontal  axis  and  enclosed  in  a  case.  When  the 
axis  and  the  vanes  attached  to  it  are  rotated  at  a  high  speed,  air 
is  drawn  in  through  openings  near  the  axis  and  is  driven  by 
centrifugal  force  into  the  case,  from  which  it  flows  into  the 
delivery-main  or  duct.  Only  low  pressures,  suitable  for  ventila- 
tion and  forced  draught,  can  be  produced  in  this  way.  But 
little  has  been  done  in  the  development  of  the  theory  or  the 
determination  of  the  practical  efficiency  of  fan-blowers.  Some 
ventilating-fans  have  their  axes  parallel  to  the  direction  of  the 
air-current,  and  the  vanes  have  a  more  or  less  helicoidal  form, 
so  that  they  may  force  the  air  by  direct  pressure;  they  are  in 
effect  the  converse  of  a  windmill,  producing  instead  of  being 
driven  by  the  current  of  air.  They  are  useful  rather  for  moving 
air  than  for  producing  a  pressure. 

Fluid  Piston- Compressors.  —  It  will  be  shown  that  the  effect 
of  clearance  is  to  diminish  the  capacity  of  the  compressor;  con- 
sequently the  clearance  should  be  made  as  small  as  possible. 
With  this  in  view  the  valves  of  compressors  and  blowers  are 
commonly  set  in  the  cylinder-heads.  Single-acting  compressors 
with  vertical  cylinders  have  been  made  with  a  layer  of  water  or 
some  other  fluid  on  top  of  the  piston,  which  entirely  fills  the 
clearance-space  when  the  piston  is  at  the  end  of  the  stroke.  An 
extension  of  this  principle  gives  what  are  known  as  fluid  piston- 
compressors.  Such  a  compressor  commonly  has  a  double-acting 
piston  in  a  horizontal  cylinder  much  longer  than  the  stroke  of 
the  piston,  thus  giving  a  large  clearance  at  each  end.  The 
clearance-spaces  extend  upward  to  a  considerable  height,  and  the 
admission-  and  exhaust- valves  are  placed  at  or  near  the  top,  and 
the  entire  clearance-space  is  filled  with  water.  The  spaces 
and  heights  must  be  so  arranged  that  when  the  piston  is  at  one 
end  of  its  stroke  the  water  at  that  end  shall  fill  the  clearance 


360  COMPRESSED   AIR 

and  cover  the  valves,  and  at  the  other  end  the  water  shall  not 
fall  to  the  level  of  the  top  of  the  cylinder.  There  are  conse- 
quently two  vertical  fluid  pistons  actuated  by  a  double-acting 
horizontal  piston.  It  is  essential  that  the  spaces  in  which  the 
fluid  pistons  act  shall  give  no  places  in  which  air  may  be  caught 
as  in  a  pocket,  and  that  there  are  no  projecting  ribs  or  other 
irregularities  to  break  the  surface  of  the  water;  and,  further, 
the  compressor  must  be  run  at  a  moderate  speed.  The  water 
forming  the  fluid  pistons  becomes  heated  and  saturated  with 
air  by  continuous  use,  and  should  be  renewed. 

Air-pumps  used  with  condensing-engines  or  for  other  purposes 
may  be  made  with  fluid  pistons  which  are  renewed  by  the 
water  coming  with  the  air  or  vapor.  In  case  the  water  thus 
supplied  is  insufficient,  water  from  without  may  be  admitted, 
or  water  from  the  delivery  may  be  allowed  to  flow  back  to 
the  admission  side  of  the  pump. 

Displacement  Compressors.  —  When  a  supply  of  water  under 
sufficient  head  is  available,  air  may  be  compressed  in  suitably 
arranged  cylinders  or  compressors  by  direct  action  of  the  water 
on  air,  compressing  it  and  expelling  it  by  displacement.  Such 
compressors  are  very  wasteful  of  power,  and  in  general  it  is 
better  to  use  water-power  for  driving  piston-compressors,  prop- 
erly geared  to  turbine-wheels  or  other  motors. 

Cooling  during  Compression.  —  There  is  always  a  considerable 
rise  of  temperature  due  to  compressing  air  in  a  piston  air-com- 
pressor, which  is  liable  to  give  trouble  by  heating,  the  cylinder 
and  interfering  with  lubrication.  Blowing-engines  which  pro- 
duce only  moderate  pressures  usually  have  their  cylinders  lubri- 
cated with  graphite,  and  no  attempt  is  made  to  cool  them.  All 
compressors  which  produce  high  pressures  have  their  cylinders 
cooled  either  by  a  water-jacket  or  by  injecting  water,  or  by 
both  methods. 

Since  the  air  after  compression  is  cooled  either  purposely  or 
unavoidably,  there  would  be  a  great  advantage  in  cooling  the 
air  during  compression,  and  thereby  reducing  the  work  of  com- 
pression. Attempts  have  been  made  to  cool  the  air  by  spray- 


MOISTURE   IN   THE   CYLINDER  361 

ing  water  into  the  cylinder,  but  experience  has  shown  that  the 
work  of  compression  is  not  much  affected  by  so  doing.  The 
only  effective  way  of  reducing  the  work  of  compression  is  to 
use  a  compound  compressor,  and  to  cool  the  air  on  the  way 
from  the  first  to  the  second  cylinder.  Three-stage  compressors 
are  used  for  very  high  pressure^.  It  is,  however,  found  that 
air  which  has  been  compressed  to  a  high  pressure  and  great 
density  is  more  readily  cooled  during  compression. 

Moisture  in  the  Cylinder.  —  If  water  is  not  injected  into  the 
cylinder  of  an  air-compressor  the  moisture  in  the  air  will  depend 
on  the  hygroscopic  condition  of  the  atmosphere.  But  even  if 
the  air  were  saturated  with  moisture  the  absolute  and  the  rela- 
tive weight  of  water  in  the  cylinder  would  be  insignificant. 
Thus  at  60°  F.  the  pressure  of  saturated  steam  is  about  one- 
fourth  of  a  pound  per  square  inch,  and  the  weight  of  one  cubic 
foot  is  about  0.0008  of  a  pound,  while  the  weight  of  one  cubic 
foot  of  air  is  about  0.08  of  a  pound.  It  is  probable  that  the 
only  effect  of  moisture  in  the  atmosphere  is  to  slightly  reduce 
the  exponent  of  the  equation  (77),  page  64.  This  conclu- 
sion probably  holds  when  the  cylinder  is  cooled  by  a  water- 
jacket. 

When  water  is  sprayed  into  the  cylinder  of  a  compressor 
the  temperature  of  the  air  and  the  amount  of  vapor  mixed  with 
it  vary,  and  there  is  no  ready  way  of  determining  its  condition. 
But,  as  has  been  stated,  the  spraying  of  water  into  the  cylinder 
does  not  much  reduce  the  work  of  compression,  and  consequently 
it  is  probable  we  can  assume  that  the  compression  always  fol- 
lows the  law  expressed  by  an  exponential  equation;  such  as 


The  value  to  be  given  to  n  is  not  well  known;  it  may  be  as 
small  as  1.2  for  a  fluid  piston-compressor,  and  it  may  approach 
i  .4  when  the  cooling  of  the  air  is  ineffective,  as  is  usually  the  case. 

Power  Expended.  —  The  indicator-diagram  of  an  air-com- 
pressor with  no  clearance-space  is  represented  by  Fig.  81.  Air 
is  drawn  in  at  atmospheric  pressure  in  the  part  of  the  cycle 


362  COMPRESSED    AIR 

of  operations  represented  by  dc\  in  the  part  represented  by  cb 
the  air  is  compressed,  and  in  the  part  represented  by  ba  it  is 
expelled  against  the  higher  pressure. 

If  pl  is  the  specific   pressure   and    vt  the 
specific  volume  of  one  pound  of  air  at  atmos- 
'        pheric  pressure,  and  p2  and   v2  corresponding 
"  quantities    at   the    higher  pressure,  then  the 

FIG.  81. 

work  done  by  the  atmosphere  on  the  piston 
of  the  compressor  while  air  is  drawn  in  is  pj)r  Assuming 
that  the  compression  curve  cb  may  be  represented  by  an  expo- 
nential curve  having  the  form 

pvn  =  pjVf  =  const., 
then  the  work  of  compression  is 

f^  .  CVldv        PU     ffoA*"1 

/  pdv  =  pp*  I     —  =  -^-^  J  (-*!        - 

J  JV2  -v       n  —  i  [  Viy 


n  -  i       p 
The  work  of  expulsion  from  b  to  a  is 


I 

n  — 1 
n 

—    I 


n  — 
n 


The  effective  work  of  the  cycle  is  therefore 


Equation  (189)  gives  the  work  done  to  compress  one  pound 
of  air,  pl  and  p2  being  specific  pressures  (in  pounds  per  square 
foot),  and  vl  the  specific  volume,  which  may  be  calculated  by 
aid  of  the  equation 


EFFECT   OF   CLEARANCE  363 

in  which  the  subscripts  refer  to  the  normal  properties  of  air  at 
freezing-point  and  at  atmospheric  pressure. 

If,  instead  of  the  specific  volume  vv  we  use  the  volume  Vl  of 
air  drawn  into  the  compressor  we  may  readily  transform  equation 
(189)  to  give  the  horse-power  directly,  obtaining 


where  p1  is  the  pressure  of  the  atmosphere  in  pounds  per  square 
inch,  and  n  is  the  exponent  of  the  equation  representing  the 
compression  curve,  which  may  vary  from  1.4  for  dry-air  com- 
pressors to  1.2  for  fluid  piston-compressors. 

Effect  of  Clearance.  —  The  indicator-diagram  of  an  air- 
compressor  with  clearance  may  be  represented  by  Fig.  82. 
The  end  of  the  stroke  expelling  air  is  at  a, 
and  the  air  remaining  in  the  cylinder  ex- 
pands from  a  to  d,  till  the  pressure  becomes 
equal  to  the  pressure  of  the  atmosphere 


before  the   next   supply  of  air  is   drawn  in.  FIG  s«. 

The  expansion  curve  ad  may  commonly  be 
represented  by  an  exponential  equation  having  the  same  expo- 
nent as  the  compression  curve  cb,  in  which  case  the  air  in  the 
clearance  acts  as  a  cushion  which  stores  and  restores  energy, 
but  does  not  affect  the  wrork  done  on  the  air  passing  through  the 
cylinder.  The  work  of  compressing  one  unit  of  weight  of  air 
in  such  a  compressor  may  be  calculated  by  aid  of  equation 
(189),  but  the  equation  (190)  for  the  horse-power  cannot  be  used 
directly. 

The  principal  effect  of  clearance  is  to  increase  the  size  of  the 
cylinder  required  for  a  certain  duty  in  the  ratio  of  the  entire 
length  of  the  diagram  in  Fig.  82  to  the  length  of  the  line  dc. 

Let  the  clearance  be   —  part  of  the  piston  displacement.     At 

the  beginning  of  the  filling  stroke,  represented  by  the  point  a, 
that  volume  will  be  filled  with  air  at  the  pressure  pr  After  the 
expansion  represented  by  ad  the  air  in  the  clearance  will  have 


364  COMPRESSED    AIR 

,the  pressure  pv  and,  assuming  that  the  expansion  follows  the 
law  expressed  by  the  exponential  equation 

pvn  =  plV* (igoa) 

its  volume  will  be 


I  (£.)' 

m\pj 


part  of  the  piston  displacement.     The  ratio  of  the  line  dc  to  the 
length  of  the  diagram  will  consequently  be 


dc        i  fp2 

—  =  i  --(7  ) 
ac  m  \ 


m 

and  this  is  the  factor  by  which  the  piston  displacement  calculated 
without  clearance  must  be  divided  to  find  the  actual  piston 
displacement. 

Temperature  at  the  End  of  Compression.  —  When  the  air  in 
the  compressor-cylinder  is  dry  or  contains  only  the  moisture 
brought  in  with  it,  it  may  be  assumed  that  the  mixture  of  air  and 
vapor  follows  the  law  of  perfect  gases, 


T       T1 
which,  combined  with  the  exponential  equation 

pvn=p1vin) 
gives 

n  —  1 


from  which  the  final  temperature  T2  at  the  end  of  compression 
may  be  determined  when  Tl  is  known.  When  water  is  used 
freely  in  the  cylinder  of  a  compressor  the  final  temperature 
cannot  be  determined  by  calculation,  but  must  be  determined 
from  tests  on  compressors. 

Contraction  after  Compression.  —  Ordinarily  compressed  air 
loses  both  pressure  and  temperature  on  the  way  from  the  com- 


VOLUME   OF   THE   COMPRESSOR   CYLINDER  365 

pressor  to  the  place  where  it  is  to  be  used.  The  loss  of  pressure 
will  be  discussed  under  the  head  of  the  flow  of  air  in  long  pipes; 
it  should  not  be  large,  unless  the  air  is  carried  a  long  distance. 
The  loss  of  temperature  causes  a  contraction  of  volume  in  two 
ways:  first,  the  volume  of  the  air  at  a  given  pressure  is  directly 
as  the  absolute  temperature;  second,  the  moisture  in  the  air 
(whether  brought  in  by  the  air  or  supplied  in  the  condenser)  in 
excess  of  that  which  will  saturate  the  air  at  the  lowest  temperature 
in  the  conduit,  is  condensed.  Provision  must  be  made  for 
draining  off  the  condensed  water.  The  method  of  estimating 
the  contraction  of  volume  due  to  the  condensation  of  moisture 
will  be  exhibited  later  in  the  calculation  of  a  special  problem. 

Interchange  of  Heat.  —  The  interchanges  of  heat  between 
the  air  in  the  cylinder  of  an  air-compressor  and  the  walls  of  the 
cylinder  are  the  converse  of  those  taking  place  between  the  steam 
and  the  walls  of  the  cylinder  of  a  steam-engine,  and  are  much 
less  in  amount.  The  walls  of  the  cylinder  are  never  so  cool  as 
the  incoming  air,  nor  so  warm  as  the  air  expelled;  consequently 
the  air  receives  heat  during  admission  and  the  beginning  of 
compression,  and  yields  heat  during  the  latter  part  of  com- 
pression and  during  expulsion.  The  presence  of  moisture  in 
the  air  increases  this  effect. 

Volume  of  the  Compressor  Cylinder.  —  Let  a  compressor 
making  n  revolutions  per  minute  be  required  to  deliver  V3  cubic 
feet  of  air  at  the  temperature  /3°  F.,  or  T3°  absolute,  and  at  the 
absolute  pressure  pa  pounds  per  square  inch,  at  the  place  where 
the  air  is  to  be  used.  Assuming  that  the  air  is  dry  when  it  is 
delivered  and  that  the  atmosphere  is  dry  when  it  is  taken  into 
the  compressor,  then  the  volume  drawn  into  the  compressor  per 
minute  at  the  temperature  T1  and  the  pressure  p^  will  be 

(193) 


cubic  feet;  and  this  expression  will  be  correct  whatever  may  be 
the  intermediate  temperatures,  pressures,  or  condition  of  satura- 
tion of  the  air. 


366  COMPRESSED   AIR 

If  the  compressor  has  no  clearance  the  piston  displacement 
will  be 


(I94) 


if  the  clearance  is  —  part  of  the  piston  displacement,  dividing 
by  the  factor  (191)  gives  for  the  piston  displacement 


2n 


expressed  in  cubic  feet. 

The  pressure  in  the  compressor-cylinder  when  air  is  drawn 
in,  is  always  less  than  the  pressure  of  the  atmosphere,  and  when 
the  air  is  expelled  it  is  greater  than  the  pressure  against  which 
it  is  delivered.  From  these  causes  and  from  other  imperfections 
the  compressor  will  not  deliver  the  quantity  of  air  calculated 
from  its  dimensions,  and  consequently  the  volume  of  the  cylinder 
as  calculated,  whether  with  o;  without  clearance,  must  be  in- 
creased by  an  amount  to  be  determined  by  experiment. 

Compound  Compressors.  —  When  air  is  to  be  compressed 
from  the  pressure  pl  to  the  pressure  p2,  but  is  to  be  delivered  at 
the  initial  temperature  tv  the  work  of  compression  may  be 
reduced  by  dividing  it  between  two  cylinders,  one  *  of  which 
takes  the  air  at  atmospheric  pressure  and  delivers  it  at  an 
intermediate  pressure  pr  to  a  reservoir,  from  which  the  other 
cylinder  takes  it  and  delivers  it  at  the  required  pressure  pv 
provided  that  the  air  be  cooled,  at  the  pressure  />',  between  the 
two  cylinders. 

The  proper  method  of  dividing  the  pressures  and  of  pro- 
portioning the  volumes  of  the  cylinders  so  that  the  work  of 
compression  may  be  reduced  to  a  minimum  may  be  deduced 
from  equation  (189)  when  there  is  no  clearance  or  when  the 
clearance  is  neglected. 


COMPOUND   COMPRESSOR  367 

The  work  of  compressing  one  pound  of  air  from  the  pressure 
pl  to  the  pressure  tf  is 


(I96) 

The  work  of  compressing  one  pound  from  the  pressure  f/  to  p2 


s 


because  the  air  after  compression  in  the  first  cylinder  is  cooled 
to  the  temperature  tl  before  it  is  supplied  to  the  second  cylinder, 
and  consequently  ptrv'  —  p^r  The  total  work  of  compression  is 

n—l  n—l 

(198) 


and  this  becomes  a  minimum  when 


— 1  n—l 

n 


becomes  a  minimum.     Differentiating  with  regard  to  />',  and 
equating  the  first  differential  coefficient  to  zero,  gives 


2    .......   (199) 

Since  the  air  is  supplied  to  each  cylinder  at  the  temperature  tl9 
their  volumes  should  be  inversely  as  the  absolute  pressures  p1 
and  p'.  This  method  also  leads  to  an  equal  distribution  of  work 
between  the  two  cylinders,  for  if  the  value  of  pf  from  equation 
(189)  is  introduced  into  equations  (197)  and  (198)  we  shall 
obtain 


.     .(,00) 


and  the  total  work  of  compression  is 


n  —  I 

W=  a*.w.-2-  M*M   '      -ij  .     . 


368  COMPRESSED   AIR 

Three-stage  Compressors.  —  When  very  high  pressures  are 
required,  as  where  air  is  used  for  storing  energy,  it  is  customary 
to  use  a  compressor  with  a  series  of  three  cylinders,  through 
which  the  air  is  passed  in  succession,  and  to  cool  the  air  on  the 
way  from  one  cylinder  to  the  next.  If  the  initial  and  final  pres- 
sures are  pl  and  pv  and  if  p'  and  p"  are  the  pressures  in  the 
intermediate  receivers  in  which  the  air  is  cooled,  the  conditions 
for  most  economical  compression  may  be  deduced  in  the  follow- 
ing way: 

The  work  of  compressing  one  pound  of  air  in  the  several 
cylinders  will  be 

n—  I 
~W  *h  ^          )     I  — '  I  \  (  \ 


W,= 


n  —  l 


But  since  the  air  is  cooled  to  the  initial  temperature  on  its  way 
from  one  cylinder  to  the  other  so  that 

piVi  =  p'v'  =  p"v"- 

the  total  work  of  compressing  one  pound  of  air  will  be 
W  =  W,  +  W2  f  W3 


This  expression  will  be  a  minimum  when 


becomes  a  minimum;  that  is,  when 

_  i 

8k        n  -  i  p'    n      n  -  i  p"    n 

jp =  —  -?a "  ~   *=i ==  °    •  •  <2o6) 


FRICTION    AND    IMPERFECTIONS 

and  -1 


_=0.    .    .  (207) 


Equations  (206)  and  (207)  lead  to 

#»  -  pjr   .......  (208) 

pm  =  p'p2  .......  (209) 

from  which  by  elimination  we  have 

.......  (210) 

and 


Since  the  temperature  is  the  same  at  the  admission  to  each 
of  the  three  cylinders,  the  volumes  of  the  cylinders  should  be 
inversely  proportional  to  the  absolute  pressures  pv  p',  and  ft'. 
As  with  the  compound  compressors,  this  method  of  arranging 
a  three-stage  compressor  leads  to  an  equal  distribution  of  work 
between  the  cylinders.  For,  if  the  values  of  p'  and  p"  from 
equations  (210)  and  (211)  are  introduced  into  equations  (202)  to 
(204),  taking  account  also  of  the  equation  (i9oa)  we  shall  have 

n  —  1 
3re  \ 

-    I         .     (212) 


and  consequently  the  total  work  of  compression  is 


n-l 


Friction  and  Imperfections.  —  The  discussion  has  thus  far 
taken  no  account  of  friction  of  the  compressor  nor  of  imperfec- 
tions due  to  delay  in  the  action  of  the  valves  and  to  heating  the 
air  as  it  enters  the  cylinder  of  the  compressor. 

From  comparisons  ol  indicator-diagrams  taken  from  the 
steam-  and  the  air-cylinders  of  certain  combined  steam-engines 
and  air-compressors  at  Paris,  Professor  Kennedy  found  a  mechan- 
ical efficiency  of  0.845.  Professor  Gutermuth  found  an  efficiency 
of  0.87  for  a  new  Riedler  compressor.  It  will  be  fair  to  assume 
an  efficiency  of  0.85  for  compressors  which  are  driven  by  steam- 


COMPRESSED   AIR 


engines ;  compressors  driven  by  turbines  will  probably  be  affected 
to  a  like  extent  by  friction. 

The  following  table  given  by  Professor  Unwin  *  shows  the 
effect  of  imperfect  valve-action  and  of  heating  the  entering  air 
as  deduced  from  tests  on  a  Dubois- Francois  compressor  which 
had  a  diameter  of  18  inches  and  a  stroke  of  48  inches. 


RATIO   OF  ACTUAL  AND   APPARENT   CAPACITIES  OF  AN 
AIR-COMPRESSOR. 


Ratio  of  air 

delivered  at 

Piston  speed, 
feet  per 
minute. 

Revolutions 
per  minute. 

atmospheric 
pressure  and 
temperature  to 
volume  dis- 

placed by 

piston  . 

80 

IO 

0.94 

160 

20 

o  .92 

200 

25 

0.90 

240 

30 

0.86 

280 

35 

0.78 

This  table  does  not  take  account  of  the  effect  of  clearance, 
nor  is  the  clearance  for  the  compressor  stated.  It  is  probable 
that  five  or  ten  per  cent  will  be  enough  to  allow  for  imperfect 
valve-action  after  the  effect  of  clearance  is  properly  calculated. 
The  effect  of  clearance  is  to  require  a  larger  volume  of  cylinder 
than  would  be  needed  without  clearance.  The  effect  of  imper- 
fect valve-action  and  of  heating  of  the  entering  air  is  to  require 
an  additional  increase  in  the  size  of  the  cylinder  of  the  air-com- 
pressor and  also  to  increase  the  work  of  compression. 

Efficiency  of  Compression.  —  If  air  could 
be  so  cooled  during  compression  that  the  tem- 
perature should  not  rise,  the  compression  line 
cb,  Fig.  83,  would  be  an  isothermal  line, 
and  the  work  of  compressing  one  pound  of  air 


FIG.  83. 


*  Development  and  Transmission  of  Power,  p,  182. 


EFFICIENCY   OF   COMPRESSION 


371 


would  be 


W 


but  plv1  =  p2v2  for  an  isothermal  change,  and  consequently 

W  =  p^  loge  ^2 (214) 

Some  investigators  have  taken  the  work  of  isothermal  com- 
pression, represented  by  equation  (214),  as  a  basis  of  comparison 
for  compressors,  and  have  considered  its  ratio  to  the  actual  work 
of  compression  as  the  efficiency  of  compression.  This  throws 
together  into  one  factor  the  effect  of  heating  during  compression 
and  .the  effect  of  imperfect  valve-action. 

Professor  Riedler  *  obtained  indicator-diagrams  from  the 
cylinders  of  a  number  of  air-compressors  and  drew  upon  them 
the  diagrams  which  would  represent  the  work  of  isothermal 
compression,  without  clearance  or  valve  losses.  A  comparison 
of  the  areas  of  the  isothermal  and  the  actual  diagrams  gave  the 
arbitrary  efficiency  of  compression  just  described.  The  following 
table  gives  his  results: 

ARBITRARY   EFFICIENCY   OF   COMPRESSION. 


Type  of  compressor. 

Pressures  in 
main, 
atmospheres. 

Lost  work  in 
per  cent  of 
useful  work. 

Arbitrary 
efficiency. 

Colladon    St   Gothard 

6 

ICX    O 

O  488 

do                             

6 

02   O 

O    £21 

Sturgeon               

•} 

04   3 

O   Cl? 

Colladon  

4 

38.  ic 

O   772 

Slide-valve                                   .... 

c 

40    3 

o  670 

Paxman    

6 

42    7 

O   7OI 

Cockerill 

6 

4O    2 

O    71  1 

Riedler  two-stage            .    .        .... 

6 

12    O7 

o  892 

A  similar  comparison  for  a  fluid  piston-compressor  showed 
an  efficiency  of  0.84. 

*  Development  and  Distribution  of  Power,  Unwin. 


372 


COMPRESSED    AIR 


There  are  three  notable  conclusions  that  may  be  drawn  from 
this  table:  (i)  there  is  much  difference  between  compressors 
working  at  the  same  pressures,  (2)  a  simple  compressor  loses 
efficiency  rapidly  as  the  pressure  rises,  and  (3)  the  compound 
or  two-stage  compressor  shows  a  great  advantage  over  a  simple 
compresson. 

Test  of  a  Blowing-Engine.  —  Pernolet  *  gives  the  following 
test  of  a  blowing-engine  used  to  produce  the  blast  for  Bessemer 
converters  at  Creusot.  The  engine  was  a  two-cylinder  horizontal 
engine,  with  the  cranks  at  right  angles.  The  piston-rod  for* 
each  cylinder  extended  through  the  cylinder-head  and  actuated 
a  double-acting  compressor.  The  dimensions  were: 

Diameter,  steam-pistons 47!  inches 

"         air-pistons 59       " 

Stroke 70.9  " 

Diameter  of  fly-wheel 26  i  feet 

At  28  revolutions  per  minute  the  following  results  were 
obtained : 

Indicated  horse-power  of  steam-cylinders  ....     1078 

"  "  ll  air-cylinders 986 

Efficiency 0.92 

Temperature  of  air  admitted 50°  F. 

"    "    delivered 140°  F. 

Pressure  of  air  delivered,  pounds  per  square     . 

inch  gauge 23.4 

Pressure  of  air  in  supply-pipe,   pounds  per 

square  inch  gauge 0.44 

At  25  revolutions  there  was  no  sensible  depression  of  pressure 
in  the  supply-pipe. 

The  air  from  such  a  blowing-engine  probably  suffers  little 
loss  of  temperature  after  compression. 

Hydraulic  Air-Compressor.  —  The  Taylor  hydraulic  air-com- 
pressor makes  use  of  water-power  for  compressing  air  at  constant 

*  L'Air   Comprime,   1876. 


HYDRAULIC    AIR-COMPRESSOR  373 

temperature.  The  essential  features  are  an  aspirator  for  charg- 
ing the  water  with  air,  a  column  of  water  to  give  the  required 
pressure,  and  a  separator  to  gather  the  air  from  the  water  after 
compression.  The  water  is  brought  to  the  compressor  in  a  pen- 
stock, as  it  would  be  to  a  water-wheel,  and  below  the  dam  it  flows 
away  in  a  ta-ilrace;  the  power  available  is  determined  from  the 
weight  of  water  flowing  and  the  head  in  the  penstock  above  the 
tailrace,  in  the  usual  manner.  Below  the  dam  a  shaft  is  exca- 
vated to  a  depth  proper  to  give  the  required  pressure  (about 
2.3  feet  depth  per  pound  pressure),  and  then  a  chamber  is  exca- 
vated to  provide  space  for  the  separator.  In  the  shaft  is  a 
plate- iron  pipe  or  cylinder,  down  which  the  water  flows;  after, 
passing  the  separator  the  water  ascends  in  the  shaft  and  flows 
away  at  the  tailrace. 

The  head  of  the  pipe  is  surrounded  by  a  vertical  plate-iron 
drum  into  which  the  penstock  leads,  so  that  water  is  supplied 
to  the  head  all  round  the  periphery.  The  head  itself  is  formed 
of  two  inverted  conical  iron-castings,  so  formed  that  the  space 
into  which  the  water  flows  at  first  contracts  and  then  expands; 
the  changes  of  velocity  being  gradual,  no  appreciable  loss  of 
energy  ensues.  At  the  throat  of  the  inlet,  where  the  velocity  is 
highest,  there  is  a  partial  vacuum,  and  air  is  admitted  through 
numerous  small  pipes  so  that  the  water  is  charged  with  bubbles 
of  air.  The  upper  conical  casting  can  be  set  by  hand  to  control 
the  supply  of  water  and  air. 

As  the  mingled  column  of  water  and  air-bubbles  goes  down 
the  pipe,  the  air  is  compressed  at  appreciably  the  temperature 
of  the  water.  At  the  lower  end,  the  pipe  expands  to  reduce  the 
velocity,  and  delivers  the  air  and  water  into  a  plate-iron  bell; 
the  air  gathers  in  the  top  of  the  bell,  from  which  it  is  led  by 
a  pipe,  and  the  water  escapes  under  the  edge  of  the  bell.  Air 
in  solution  is  unavoidably  lost,  and  forms  the  chief  source  of 
loss  of  power  in  the  device.  The  air  is,  of  course,  saturated  with 
moisture  at  the  temperature  of  the  water,  but  that  is  probably 
the  condition  of  compressed  air  however  produced.  The 
efficiency  of  the  compressor  may  be  taken  as  about  0.60  to 


374 


COMPRESSED    AIR 


0.70;  making  allowance  for  loss  in  transmission  and  for  the 
efficiency  of  the  compressed-air  motors,  the  system  appears  to 
be  inferior  to  the  ordinary  turbine  water-wheel. 

Air- Pumps.  —  The  feed-water  supplied  to  a  steam-boiler 
usually  contains  air  in  solution,  which  passes  from  the  boiler 
with  the  steam  to  the  engine  and  thence  to  the  condenser.  In 
like  manner  the  injection-water  supplied  to  a  jet-condenser 
brings  in  air  in  solution.  Also  there  is  more  or  less  leakage  of 
air  into  the  cylinder  communicating  with  the  condenser  and 
into  the  exhaust-pipe  or  the  condenser  itself.  An  air-pump 
must  therefore  be  provided  to  remove  this  air  and  to  maintain 
the  vacuum.  The  air-pump  also  removes  the  condensed  steam 
from  a  surface-condenser,  and  the  mingled  condensed  steam  and 
injection-water  from  a  jet-condenser.  If  no  air  were  brought 
into  the  condenser  the  vacuum  would  be  maintained  by  the  con- 
densation of  the  steam  by  the  injection,  or  the  cooling  water, 
and  it  would  be  sufficient  to  remove  the  water  by  a  common 
pump,  which,  with  a  surface-condenser,  might  be  the  feed- 
pump. 

The  weight  of  injection-water  per  pound  of  steam,  calculated 
by  the  method  on  page  149,  will  usually  be  less  than  20  pounds, 
but  it  is  customary  to  provide  30  pounds  of  injection -water  per 
pound  of  steam,  with  some  method  of  regulating  the  quantity 
delivered. 

It  may  be  assumed  that  the  injection-water  will  bring  in  with 
it  one-twentieth  of  its  volume  of  air  at  atmospheric  pressure, 
and  that  this  air  will  expand  in  the  condenser  to  a  volume  inversely 
proportional  to  the  absolute  pressure  in  the  condenser.  The 
capacity  of  the  air-pump  must  be  sufficient  to  remove  this  air 
and  the  condensed  steam  and  injection-water. 

An  air-pump  for  use  with  a  surface-condenser  may  be  smaller 
than  one  used  with  a  jet-condenser.  In  marine  work  it  is  com- 
mon to  provide  a  method  of  changing  a  surface-  into  a  jet-con- 
denser, and  to  make  the  air-pump  large  enough  to  give  a  fair 
vacuum  in  case  such  a  change  should  become  advisable  in  an 
emergency. 


DRY-AIR   PUMP 


375 


Seaton  *  states  that  the  efficiency  of  a  vertical  single-acting 
air-pump  varies  from  0.4  to  0.6,  and  that  of  a  double-acting 
horizontal  air-pump  from  0.3  to  0.5,  depending  on  the  design 
and  condition;  that  is,  the  volume  of  air  and  water  actually 
discharged  will  bear  such  ratios  to  the  displacement  of  the 
pump. 

He  also  gives  the  following  table  of  ratios  of  capacity  of  air- 
pump  cylinders  to  the  volume  of  the  engine  cylinder  or  cylinders 
discharging  steam  into  the  condenser : 


RATIO    OF   ENGINE   AND    AIR-PUMP   CYLINDERS. 


Description  of  Pump. 

Description  of  Engine. 

Ratio. 

Single-acting  vert  cal     .... 

Jet-condensing,  expansion  i|  to  2 

6  to    8 

i                   f 

Surface-     "                             i|  to  2 

8  to  10 

i                   i 

Jet-                                           3  to  5 

10  to  12 

1                   '            .... 

Surface-     "                              3  to  5 

12  to  15 

'                   '            .... 

compound    .    .    . 

15  to  18 

Double-acting  horizontal  .    .    . 

Jet-condensing,  expansion    i^  to  2 

10  to  13 

'                     "... 

Surface-     "                "           i|  to  2 

13  to  16 

<                      « 

Jet-            "                "             3  to  5 

16  to  19 

'                     "... 

Surface-     "                              3  to  5 

19  to  24 

... 

"           "         compound     .    .    . 

24  to  28 

Dry-air  Pump.  —  In  the  recent  development  of  steam-engineer- 
ing, especially  for  steam-turbines,  great  emphasis  is  given  to 
obtaining  a  high  vacuum.  For  this  purpose  the  old  form  of  air- 
pump  which  withdraws  air  and  water  from  the  condenser  has 
been  replaced  by  a  feed-pump  which  takes  water  only  from  the 
condenser,  and  a  dry-air  pump  which  removes  the  air.  The  air 
is  necessarily  saturated  with  moisture  at  the  temperature  in 
the  condenser,  and  allowance  must  be  made  for  this  moisture  or 
steam,  in  the  design  of  the  pump.  For  this  purpose  Dalton's  law 
is  used,  which  says  that  the  total  pressure  in  any  receptacle  con- 
taining air  and  vapor  is  equal  to  the  sum  of  the  pressures  due 
to  the  air  and  to  the  vapor. 

*  Manual  of  Marine  Engineering, 


•576  COMPRESSED   AIR 

If  the  amount  of  air  brought  by  the  water  to  a  jet-condenser 
can  be  determined  or  assumed,  a  calculation  for  a  dry-air  pump 
can  readily  be  made.  The  leakage  to  a  surface-condenser  can- 
not be  estimated,  and  consequently  the  only  way  of  proportion- 
ing the  air-pump  for  a  surface-condenser  is  that  already  given 
on  page  375. 

To  illustrate  the  method  of  calculation  for  a  dry-air  pump 
use  will  be  made  of  the  data  from  the  test  of  the  Chestnut  Hill 
Pumping  Station  already  quoted  on  page  239. 

The  vacuum  in  the  condenser  was  27.25  inches  of  mercury, 
and  the  barometer  stood  at  30.25  inches  reduced  to  32°  F.,  so 
that  the  absolute  pressure  was  1.47  of  a  pound.  The  condensing 
water  entered  the  surface-condenser  at  5i°.9  F.  and  left  at 
85°. 2  F. ;  had  there  been  a  jet-condenser  this  would  have  been  the 
temperature  in  the  condenser  and  will  be  used  for  our  calculation. 
Making  use  of  the  equation  for  the  quantity  of  condensing  water 
on  page  150,  we  have, 

;  1111.2-53.3 
53-3  -  20 

Since  the  engine  used  11.22  pounds  of  steam  per  horse-power 
per  hour  and  developed  575.7  horse-power,  the  total  condensing 
water  per  hour  would  be 

32  X  II  22  X  575.7  = 

the  denominator  being  the  weight  of  a  cubic  foot  of  water.  If 
the  water  brings  one-twentieth  of  its  volume  of  atmospheric 
air,  the  volume  of  air  will  be  166  cubic  feet  per  hour. 

Steam  at  85°.  2  F.  has  the  pressure  of  0.598  of  a  pound  abso- 
lute; consequently  the  pressure  1.47  of  a  pound  in  the  con- 
denser is  made  up  of  0.598  steam-pressure  and  0.872  air-pressure. 
The  atmospheric  pressure  is  30.25  inches  of  mercury  or  14.85 
pounds,  so  that  taking  account  of  the  influence  of  the  pressures 
and  absolute  temperatures  the  volume  of  air  (saturated  with 
moisture)  to  be  removed  from  the  condenser  per  hour  is 


CALCULATION   FOR  AN   AIR   COMPRESSOR  377 


I66  x  459.5  +  85.2  x  1^85  ^        cub.c  feet 

459-5  +  5J-9     0-872 

Assuming  the  air-pump  to  be  single-acting  and  to  be  con- 
nected directly  to  the  engine  which  made  about  50  revolutions 
per  minute,  the  effective  displacement  of  the  air-pump  bucket 
should  be 

3010  -f-  (50  X  60)  =1.0  cubic  foot. 

To  allow  for  the  effect  of  the  air-pump  clearance,  imperfection 
of  valve-action,  and  for  variation  in  the  temperature  of  condens- 
ing water,  this  quantity  may  be  increased  by  50  to  100  per  cent. 

The  engine  had  3^  feet  for  the  diameter  and  6  feet  for  the 
stroke  of  the  low-pressure  piston,  so  that  its  displacement  was 
nearly  50  cubic  feet;  the  air-pump  had  a  diameter  of  2  feet  and 
a  stroke  of  one  foot,  so  that  its  displacement  was  3.14  cubic 
feet;  the  ratio  of  displacements  was  about  sixteen.  This  discrep- 
ancy shows  that  the  conventional  method  of  designing  air-pumps 
provides  liberal  capacity. 

Calculation  for  an  Air  Compressor.  —  Let  it  be  required  to  find 
the  dimensions  of  an  air-compressor  to  deliver  300  cubic  feet  of 
air  per  minute  at  100  pounds  per  square  inch  by  the  gauge,  and 
also  the  horse-power  required  to  drive  it. 

If  it  is  assumed  that  the  air  is  forced  into  the  delivery-pipe 
at  the  temperature  of  the  atmosphere,  and,  further,  that  there 
is  no  loss  of  pressure  between  the  compressor  and  the  delivery- 
pipe,  equation  (193)  for  finding  the  volume  drawn  into  the 
compressor  will  be  reduced  to 

Vl  =  V3  —  3  =  300  X  —  "  =  2341  cubic  feet. 
Pi  I4-7 

If  now  we  allow  five  per  cent  for  imperfect  valve-action  and 
for  heating  the  air  as  it  is  drawn  into  the  compressor  the  appar- 
ent capacity  of  the  compressor  will  be 

2341  -f-  0.95  =  2464  cubic  feet. 

This  is  the  volume  on  which  the  power  for  the  compressor  must 
be  calculated. 


378  COMPRESSED    AIR 

If  the  clearance  of  the  compressor  is  0.02  of  the  piston  dis- 
placement, then  the  factor  for  allowing  for  clearance  will  be 


_L(*,y+ '--i --*-( 

m  V^,/       m  100  \ 


2 
—   =  0.9332 


14.77         100 

if  the  exponent  of  the  equation  representing  the  expansion  of 
the  air  in  the  clearance  is  1.4.     Consequently  the  volume  on 
which  the  dimensions  of  the  compressor  must  be  based  is 
2464  -7-  0.9332  =  2640  cubic  feet. 

At  80  revolutions  per  minute  the  mean  piston  displacement 
will  be 

2640  -T-  (2  X  80)  =  16.5  cubic  feet. 

Assuming  a  stroke  of  3  feet,  the  mean  area  of  the  piston  must  be 
(144  X  16.5)  -T-  3  =  792  square  inches. 

Allowing  1 6  square  inches  for  a  piston-rod  4^  inches  in  diameter 
gives  a  mean  area  of  800  square  inches  for  the  piston,  which 
corresponds  very  nearly  to  32  inches  for  the  diameter  of  the 
piston. 

The  power  expended  in  the  compressor-cylinder  may  be  cal- 
culated by  equation  (190),  using  for  Vl  the  apparent  capacity 
of  the  compressor,  giving 

1.4  —  1 

H  P    =  144  X  14.7  X  2464  X  1.4  (  fll±l\  U  _  T  ) 
33000  X  (1.4  —  i)        I  \  14-7'  ) 

If  the  friction  of  the  combined  steam-engine  and  compressor 
is  assumed  to  be  15  per  cent  the  horse-power  of  the  steam- 
cylinder  must  be 

442  -T-  0.85  =  520. 

If  the  temperature  of  the  atmosphere  drawn  into  the  com- 
pressor is  70°  F.,  then  by  an  equation  like  (80),  page  65,  the 
delivery  temperature  will  be 

n  —  1  1.4-1 


absolute,  or  about  493°  F. 


CALCULATION   FOR   AN   AIR   COMPRESSOR  379 

The  calculation  has  been  carried  on  for  a  simple  compressor, 
but  there  will  be  a  decided  advantage  in  using  a  compound  com- 
pressor for  such  work.  Such  a  compressor  should  have  for  the 
pressure  in  the  intermediate  reservoir 


Pf  =  \S~PiP2  =  v/n4-7  X  14.7  =  41.06  pounds. 
The   factor  for  allowing  for  clearance   of  the   low-pressure 

cylinder  will  now  be 

i^  _i 

i  (p'Y      i  2    /4i.o6V'4  ,      2 

i  --    £      +  -  =  i  --  (-  -  J     +  —  =  0.9784. 
m\pj       m  100  \  14.77          100 

The  loss  from  imperfect  action  of  the  valves  and  for  heating 
of  the  air  as  it  enters  the  compressor  will  be  less  for  a  compound 
than  for  a  simple  compressor,  but  we  will  here  retain  the  value 
2464  cubic  feet,  previously  found  for  the  apparent  capacity  of 
the  compressor.  The  volume  from  which  the  dimensions  of  the 
compressor  will  be  found  will  now  be 

2464  -T-  0.9784  =2518  cubic  feet, 

which  with  80  revolutions  per  minute  will  give  15.74  cubic  feet 
for  the  piston  displacement,  and  755.5  square  inches  for  the 
effective  piston  area,  if  the  stroke  is  made  3  feet,  as  before. 
Adding  16  inches  for  the  piston-rod,  which  will  be  assumed  to 
pass  entirely  through  the  cylinder,  will  give  for  the  diameter  of 
the  low-pressure  cylinder  31!  inches. 

Since  the  pressure  pf  is  a  mean  proportional  between  pl  and 
p2,  the  clearance  factor  for  the  high-pressure  cylinder  will  be 
the  same  as  that  for  the  low-pressure  cylinder,  and,  as  the  volumes 
are  inversely  proportional  to  the  pressures  pl  and  /,  the  high- 
pressure  piston  displacement  will  be 

(15.74  X  14.7)  -*•  41.06  =  5.64  cubic  feet. 

If  we  allow  8  inches  for  a  rod  4%  inches  in  diameter  at  one  side 
of  the  piston,  then  the  mean  area  of  the  piston  will  be  278.7 
square  inches,  which  corresponds  to  a  diameter  of  i8f-  inches 
for  the  high-pressure  cylinder.  In  reality  the  piston-rod  for  the 
compound  compressor  may  have  a  less  diameter  than  the  rod  for 


380  COMPRESSED   AIR 

a  simple  compressor,  because  the  maximum  pressure  on  both 
pistons  will  be  less  than  that  for  the  piston  of  the  simple  com- 
pressor. Again,  the  rod  which  extends  from  the  large  to  the 
small  piston  may  be  reduced  in  size.  But  details  like  these 
which  depend  on  the  calculation  of  strength  cannot  properly 
receive  much  attention  at  this  place. 

The  power  required  to  drive  the  compressor  may  be  derived 
from  equation  (190),  replacing  vv  the  specific  volume,  by  Vv 
the  apparent  capacity  of  the  low-pressure  cylinder.  Using  the 
apparent  capacity  already  obtained,  2464  cubic  feet,  we  have 
for  the  power  expended  in  the  air-cylinders 

up         2  X  144  X  14.7  X  2464  X  1.4  .  , 

33000  X  (1.4 -i)        ~\\w)  iJ-3775 

and,  as  before,  allowing  15  per  cent  for  friction  of  the  engine 
and  compressor,  we  have  for  the  indicated  horse-power  of  the 
steam-engine 

377  -T-  0.85  =  444. 

The  temperature  at  the  delivery  from  the  low-pressure  cylinder 
will  be  for  70°  F.  atmospheric  temperature 

1.4-1 
1.4 


N/4i.o6\  IA 
(46o+7o)^         J        =7II 


absolute,  or  251°  F.  Since  ft  is  a  mean  proportional  between 
p1  and  p2,  this  will  also  be  the  temperature  of  the  air  delivered 
by  the  high-pressure  cylinder. 

Friction  of  Air  in  Pipes.  —  The  resistance  to  the  flow  of  a 
liquid  through  a  pipe  is  represented  in  works  on  hydraulics  by 
an  expression  having  the  form 

^   I 

? (215) 

2g  m 

in  which  ?  is  an  experimental  coefficient,  u  is  the  velocity  in 
feet  per  second,  g  is  the  acceleration  due  to  gravity,  /  is  the 
length  of  the  pipe  in  feet,  and  m  is  the  hydraulic  mean  depth, 


FRICTION   OF   AIR  IN    PIPES  381 

which  last  term  is  obtained  by  dividing  the  area  of  the  pipe 
by  its  perimeter.     For  a  cylindrical  pipe  we  have  consequently 


m  =  ±nd?  -*-  TttZ  =  id  ......  (216) 

The  expression  (215)  represents  the  head  of  liquid  required  to 
overcome  the  resistance  of  friction  in  the  pipe  when  the  velocity 
of  flow  is  u  feet  per  second.  Such  an  expression  cannot  properly 
be  applied  to  flow  of  air  through  a  pipe  when  there  is  an  appre- 
ciable loss  of  pressure,  for  the  accompanying  increase  in  volume 
necessitates  an  increase  of  velocity,  whereas  the  expression  treats 
the  velocity  as  a  constant.  If,  however,  we  consider  the  flow 
through  an  infinitesimal  length  of  pipe,  for  which  the  velocity 
may  be  treated  as  constant,  we  may  write  for  the  loss  of  head 
due  to  friction 

ru2  dl 

?  --    ........  (217) 

2g  m 

This  loss  of  head  is  the  vertical  distance  through  which  the  air 
must  fall  to  produce  the  work  expended  in  overcoming  friction, 
and  the  total  work  thus  expended  may  be  found  by  multiplying 
the  loss  of  head  by  the  weight  of  air  flowing  through  the  pipe. 
It  is  convenient  to  deal  with  one  pound  of  air,  so  that  the  expres- 
sion for  the  loss  of  head  also  represents  the  work  expended. 

The  air  flowing  through  a  long  pipe  soon  attains  the  tem- 
perature of  the  pipe  and  thereafter  remains  at  a  constant  temper- 
ature, so  that  our  discussion  for  the  resistance  of  friction  may  be 
made  under  the  assumption  of  constant  temperature,  which 
much  simplifies  our  work,  because  the  intrinsic  energy  of  the  air 
remains  constant.  Again,  the  work  done  by  the  air  on  enter- 
ing a  given  length  dl  will  be  equal  to  the  work  done  by  the  air 
when  it  leaves  that  section,  because  the  product  of  the  pressure 
by  the  volume  is  constant. 

Since  there  is  a  continual  increase  of  volume  corresponding 
to  the  loss  of  pressure  to  overcome  friction,  and  consequently 
a  continual  increase  of  velocity  from  the  entrance  to  the  exit 
end  of  the  pipe,  there  is  also  a  continual  gain  of  kinetic  energy. 


382  COMPRESSED   AIR 

But  the  velocity  of  air  in  long  pipes  is  small,  and  the  changes  of 
kinetic  energy  can  be  neglected. 

The  air  expands  by  the  amount  dv  as  it  passes  through  the 
length  dl  of  pipe,  and  each  pound  does  the  work  pdv.  This 
work  must  be  supplied  by  the  loss  of  head,  and,  since  there  is 
no  other  expenditure  of  energy,  the  work  expended  in  the  loss 
of  head  is  equal  to  the  work  done  by  expansion;  consequently 

.  ,         yu2  dl  .     _. 

pdv  =  ? (218) 

2g  m 

But  from  the  characteristic  equation 

pv  =  RT (219) 


we  have 


RT  . 
=--  -  —  dp, 


which  substituted  in  equation  (217)  gives 

<,u2dl  RT  , 

%  --  =  --  —dp       ....    (220) 
2gm  p 

If  the  area  of  the  pipe  is  A  square  feet,  and  if  W  pounds  of  air 
flow  through  it  per  second,  then 

Wv        WRT 

—    ~AT  ......  (22I) 

in  which  v  is  the  specific  volume,  for  which  a  value  may  be 
derived  from  equation  (219).  Replacing  u  in  equation  (220) 
by  the  value  just  derived,  we  have 

RT, 


(222) 


2gA2p2m 
W2dl 


Integrating  between  the  limits  L  and  o,  and  p2  and  pv  we 
have 

o   W2L        p,2  -  p,2 
-          = 


FRICTION    OF   AIR   IN    PIPES  383 

But  from  equation  (221)  the  velocity  at  the  entrance  to  the  pipe 
where  the  pressure  is  pl  will  be 

WRT         .     _,_      Ap.u, 

MI=__  and  w  =  -jf, 

so  that  equation  (223)  may  be  reduced  to 

f  A'p,*u,'L       p?  -  p*  _ 
*  gA'mKT*  RT 

.....  «-> 

Equation  (224)  may  be  solved  as  follows  : 

(gRTmp'-p*)  . 

1  2      ' 


The  first  two  forms  allow  us  to  calculate  either  the  velocity 
or  the  loss  of  pressure;  the  last  form  may  be  used  to  calculate 
values  of  f  from  experiments  on  the  flow  through  pipes. 

From  experiments  made  by  Riedler  and  Gutermuth*  Pro- 
fessor Unwin  f  deduces  the  following  values  for  ?: 

Diameter  of  pipe,  feet.  £    • 

0.492  0.00435 

0.656  0.00393 

0.980  0.00351 

For  pipes  over  one  foot  in  diameter  he  recommends  for  use 

?  =  0.003. 

*  Neue  Erfahrungen  iiber  die  Kraftversorgung  von  Paris  durch  Drttckluft,  1891. 
f  Development  and  Distribution  of  Power. 


384  COMPRESSED   AIR 

Replacing  the  hydraulic  mean  depth  m  by  id,  its  value  for 
round  pipes,  and  using  R  =  53.22  and  g  =  32.16,  we  have  in 
place  of  equation  (226) 

All  of  the  dimensions  are  given  in  feet,  but  from  the  form  of 
the  equation  it  is  evident  that  the  pressures  may  be  in  any  con- 
venient units,  for  example,  in  pounds  per  square  inch  absolute. 

For  example,  let  us  find  the  loss  of  pressure  of  300  cubic  feet 
per  minute  if  delivered  through  a  six-inch  pipe  a  mile  long,  the 
initial  pressure  being  100  pounds  by  the  gauge. 

The  velocity  of  the  air  will  be 

irrP  _   /   6    \2 

r  /•      \  7t(.l  7i   I  13 1  r 

(300  -T-  60)  -T-  —  =  5  -j- 25.5  feet. 

4  4 

The  terminal  pressure  will  consequently  be 

_  0.0044  X  25.5    X  5280  )* 
430  (460  +  70) i       ) 

=  107  pounds, 

with  70°  F.  for  the  temperature  of  the  atmosphere  and  with 

£  =  0.0044.     Consequently  the  loss  of  pressure  is  about  eight 

pounds. 

Compressed-air  Engines.  —  Engines  for  using  "compressed  air 

differ  from  steam-engines  only  in  details  that  depend  on  the 

nature  of  the  working 
fluid.  In  some  instances 
compressed  air  has  been 
used  in  steam-engines 
without  any  change;  for 
example,  in  Fig.  84  the 
dotted  diagram  was  taken 
from  the  cylinder  of  an 
FIG.  84.  engine  using  compressed 

air,  and  the  dot-and-dash 

diagram  was  taken  from  the  same  end  of  the  cylinder  when 


FINAL  TEMPERATURE  385 

steam  was  used  in  it.  The  full  line  ab  is  a  hyperbola,  and  the 
line  ac  is  the  adiabatic  line  for  a  gas;  both  lines  are  drawn  through 
the  intersection  of  the  expansion  lines  of  the  two  diagrams. 

Power  of  Compressed-air  Engines.  —  The  probable  mean 
effective  pressure  attained  in  the  cylinder  of  a  compressed-air 
engine,  or  to  be  expected  in  a  projected  engine, 
may  be  found  in  the  same  manner  as  is 
used  in  designing  a  steam-engine.  In  Fig. 
85  the  expansion  curve  i  2  and  the  com- 
pression curve  3  o  may  be  assumed  to  be 
adiabatic  lines  for  a  gas  represented  by 
the  equation 


and  the  area  of  the  diagram  may  be  found  in  the  usual  way,  and 
therefrom  the  mean  effective  pressure  can  be  determined.  Hav- 
ing the  mean  effective  pressure,  the  power  of  a  given  engine  or 
the  size  required  for  a  given  power  may  be  determined  directly. 
The  method  will  be  illustrated  later  by  an  example. 

Air-  Consumption.  —  The  air  consumed  by  a  given  compressed- 
air  engine  may  be  calculated  from  the  volume,  pressure,  and 
temperature  at  cut-off  or  release,  and  the  volume,  temperature, 
and  pressure  at  compression,  in  the  same  way  that  the  indicated 
consumption  of  a  steam-engine  is  calculated;  but  in  this  case 
the  indicated  and  actual  consumption  should  be  the  same,  since 
there  is  no  change  of  state  of  the  working  fluid.  Since  the 
intrinsic  energy  of  a  gas  is  a  function  of  the  temperature  only, 
the  temperature  will  not  be  changed  by  loss  of  pressure  in  the 
valves  and  passages,  and  the  air  at  cut-off  will  be  cooler  than 
in  the  supply-pipe,  only  on  account  of  the  chilling  action  of  the 
walls  of  the  cylinder  during  admission,  which  action  cannot  be 
energetic  when  the  air  is  dry,  and  probably  is  not  very  important 
when  the  air  is  saturated. 

Final  Temperature.  —  If  the  expansion  in  a  compressed-air 
engine  is  complete,  i.e.,  if  it  is  carried  down  to  the  pressure  in 
the  exhaust-pipe,  then,  assuming  that  there  are  no  losses  of 


COMPRESSED   AIR 


pressure  in  valves  and  passages,  the  final  temperature  may  be 
found  by  the  equation 


(229) 


If  the  expansion  is  not  complete,  then  the  temperature  at  the 
end  of  expansion  may  be  found  by  the  equation 

TV-r.^Y"1.  .(230) 


in  which  Ve  is  the  volume  in  the  cylinder  at  cut-off  and  Vr  at 
release,  Tr  is  the  absolute  temperature  at  the  end  of  expansion, 
and  Ts  is  the  temperature  at  cut-off,  assumed  to  be  the  same  as 
in  the  supply-pipe.  Tr  is  not  the  temperature  during  back- 
pressure nor  in  the  exhaust-pipe.  When  the  exhaust-valve  is 
opened  at  release  the  air  will  expand  suddenly,  and  part  of  the 
air  will  be  expelled  at  the  expense  of  the  energy  in  the  air  remain- 
ing —  much  as  though  that  air  expanded  behind  a  piston,  and 
the  temperature  in  the  cylinder  during  exhaust  and  at  the 
beginning  of  compression  may  be  calculated  by  equation  (229). 
The  temperature  in  the  exhaust-pipe  will  not  be  so  low,  for  the 
temperature  of  the  escaping  air  will  vary  during  the  expulsion 
produced  by  sudden  expansion,  and  will  only  at  the  end  of  that 
operation  have  the  temperature  J"4,  while  the  energy  expended 
on  that  air  to  give  it  velocity  will  be  restored  when  the  velocity 
is  reduced  to  that  in  the  exhaust-pipe. 

Volume  of  the  Cylinder.  —  The  determination  of  the  volume 
of  the  cylinder  of  a  compressed-air  engine  which  uses  a  stated 
volume  of  air  per  minute  is  the  converse  of  the  determination 
of  the  air  consumed  by  a  given  engine,  and  can  be  found  by  a 
similar  process.  We  may  calculate  the  volume  of  air,  at  the 
pressure  in  the  supply-pipe,  consumed  per  stroke  by  an  engine 
having  one  unit  of  volume  for  its  piston  displacement,  and 
therefrom  find  the  number  of  units  of  volume  of  the  piston  dis- 
placement for  the  required  engine. 

Interchange  of  Heat.  —  The  interchanges   of  heat  between 


MOISTURE   IN   THE   CYLINDER  387 

the  walls  of  the  cylinder  of  a  compressed-air  engine  and  the  air 
working  therein  are  of  the  same  sort  as  those  taking  place  between 
the  steam  and  the  walls  of  the  cylinder  of  a  steam-engine;  that 
is  to  say,  the  walls  absorb  heat  during  admission  and  compression 
if  the  latter  is  carried  to  a  considerable  degree,  and  yield  heat 
during  expansion  and  exhaust.  Since  the  walls  of  the  cylinder 
are  never  so  warm  as  the  entering  air  nor  so  cold  as  the  air 
exhausted,  the  walls  may  absorb  heat  during  the  beginning  of 
expansion  and  yield  heat  during  the  beginning  of  compression. 

The  amount  of  interchange  of  heat  is  much  less  in  a  com- 
pressed-air engine  than  in  a  steam-engine.  With  a  moderate 
expansion  the  interchanges  of  heat  between  dry  air  and  the 
walls  of  the  cylinder  are  insignificant.  Moisture  in  the  air 
increases  the  interchanges  in  a  marked  degree,  but  does  not 
make  them  so  large  that  they  need  be  considered  in  ordinary 
calculations. 

Moisture  in  the  Cylinder.  —  The  chief  disadvantage  in  the 
use  of  moist  compressed  air  —  and  it  is  fair  to  assume  that 
compressed  air  is  nearly  if  not  quite  saturated  when  it  comes 
to  the  engine  —  is  that  the  low  temperature  experienced  when 
the  range  of  pressures  is  considerable  causes  the  moisture  to 
freeze  in  the  cylinder  and  clog  the  exhaust-valves.  The  diffi- 
culty may  be  overcome  in  part  by  making  the  valves  and  passages 
of  large  size.  Freezing  of  the  moisture  may  be  prevented  by 
injecting  steam  or  hot  water  into  the  supply-pipe  or  the  cylinder, 
or  the  air  may  be  heated  by  passing  it  through  externally  heated 
pipes  or  by  some  similar  device.  In  the  application  of  com- 
pressed air  to  driving  street-cars  the  air  from  the  reservoir  has 
been  passed  through  hot  water,  and  thereby  made  to  take  up 
enough  hot  moisture  to  prevent  freezing..  The  study  of  gas- 
engines  suggests  a  method  of  heating  compressed  air  which  it  is 
believed  has  never  been  tried.  The  air  supplied  to  a  compressed- 
air  engine,  or  a  part  of  the  air,  could  be  caused  to  pass  through 
a  lamp  of  proper  construction  to  give  complete  combustion,  and 
the  products  of  combustion  passed  to  the  engine  with  the  air. 
Should  such  a  device  be  used  it  would  be  advisable  that  the  tern- 


388  COMPRESSED   AIR 

perature  of  the  air  should  be  raised  only  to  a  moderate  degree 
to  avoid  destruction  of  the  lubricants  in  the  cylinder,  and  the 
combustion  at  all  hazards  must  be  complete,  or  the  cylinder 
would  be  fouled  by  unburned  carbon. 

Compound  Air-Engines..  —  When  air  is  expanded  to  a  con- 
siderable degree  in  a  compressed-air  engine  a  gain  may  be 
realized  by  dividing  the  expansion  into  two  or  more  stages  in 
as  many  cylinders,  provided  that  the  air  can  be  economically 
reheated  between  the  cylinders.  The  heat  of  the  atmosphere 
or  of  water  at  the  same  temperature  may  sometimes  be  used 
for  this  purpose.  It  is  not  known  that  machines  of  this  con- 
struction have  been  used.  If  they  were  to  be  constructed  the 
practical  advantages  of  equal  distribution  of  work  and  pressure 
would  probably  control  the  ratio  of  the  volumes  of  the  cylinders. 

Calculation  for  a  Compressed-air  Engine.  —  Let  it  be  required 
to  find  the  dimensions  for  a  compressed-air  engine  to  develop 
100  indicated  horse-power  at  the  pressure  of  92  pounds  by  the 
gauge  and  at  70°  F.  Assume  the  clearance  to  be  five  per  cent 
of  the  piston  displacement,  and  assume  the  cut-off  to  be  at 
quarter  stroke,  the  release  to  be  at  the  end  of  the  stroke,  and  the 
compression  at  one-tenth  of  the  stroke. 

If  the  piston  displacement  is  represented  by  Z),  then  the  volume 
in  the  cylinder  at  cut-off  will  be  0.30  Z),  that  at  release  will  be 
1.05  D,  and  that  at  compression  will  be  0.15  D.  The  absolute 
pressures  during  supply  and  exhaust  may  be  assumed  to  be 
106.7  and  14.7  pounds  per  square  inch.  The  work  for  one 
stroke  of  the  piston  will  be 


IT/  T-»   ,  144X106.  7  Xo.^oD  (         /o^oV'4"1) 

PF=  144X106.  7  Xo.25Z?  +  —  -  --  -  -  -  —  ]  i  —  (—  —  1 

ic  -i  I         \i.o$/         $ 

n       144  X  14.7  X  o.i5Z>  (         /o.osV4"1   ) 
-i44X.i4.7Xo.9Z7-  -^-—         -ji-fejj          j 

=  I44D  (26.68  +  31.530  -  13.23  -  1.96)  =  144  X  43-02£>. 

The  corresponding  mean  effective  pressure  is  43.02  pounds  per 
square  inch.     If  the  engine  is  furnished  with  large  ports  and 


CALCULATION    FOR   A   COMPRESSED-AIR   ENGINE        389 

automatic  valve-gear  the  actual  mean  effective  pressure  may 
be  0.9  of  that  just  calculated,  or  38.7  pounds  per  square  inch. 

For  a  piston  displacement  D  the  engine  will  develop  at  150 
revolutions  per  minute 

144  X  38.7.0  X  2  X  iso  , 

— -^ — '- 2—  horse-power; 

33000 

and  conversely  to  develop  100  horse-power  the  piston  displace- 
ment must  be 

~               100  X  33000  ,  .     . 

D= ^ =  i. 974  cubic  feet, 

144  X  38.7  X  2  X  150 

and  with  a  stroke  of  2  feet  the  effective  area  of  the  piston  will  be 
1.974  X  144  -*-  2  =  142.1  square  inches. 

If  the  piston-rod  is  2  inches  in  diameter  it  will  have  an  area  of 
3.14  square  inches,  so  that  the  mean  area  of  the  piston  will  be 
143.7  square  inches,  corresponding  to  a  diameter  of  13^  inches. 

We  find,  consequently,  that  an  engine  developing  100  horse- 
power under  the  given  conditions  will  have  a  diameter  of  13 J 
inches  and  a  stroke  of  2  feet,  provided  that  it  runs  at  150  revo- 
lutions per  minute. 

In  order  to  determine  the  amount  of  air  used  by  the  engine 
we  must  consider  that  the  air  caught  at  compression  is  compressed 
to  the  full  admission-pressure  of  106.7  pounds  absolute.  Part 
of  this  compression  is  done  by  the  piston  and  part  by  the  entering 
air,  but  for  our  present  purpose  it  is  immaterial  how  it  is  done. 
The  volume  filled  by  air  at  atmospheric  pressure  when  the 
exhaust- valve  closes  (including  clearance)  is  0.15  of  the  piston 
displacement.  When  the  pressure  is  increased  to  106.7  pounds 
the  volume  will  be  reduced  to 


0.15  I —      I    =  0.017 

of  the  piston  displacement.     The  volume  drawn  in  from  the 
supply-pipe  will  consequently  be 

0.25  -f  0.05  —  0.017  =  0.283 


390  COMPRESSED    AIR 

of  the  piston  displacement.  If  the  compression  occurred  suffi- 
ciently early  to  raise  the  pressure  to  that  in  the  supply-pipe 
before  the  admission- valve  opened,  then  only  0.25  of  the  piston 
displacement  would  be  used  per  stroke  and  a  saving  of  about  13 
per  cent  would  be  attained;  in  such  case  the  mean  effective 
pressure  would  be  smaller  and  the  size  of  the  cylinder  would  be 
larger. 

The  air-consumption  for  the  engine  appears  to  be 
2  X  150  X  0.283  X  pist-  displ.  =2X150X0.283X1.974=  167.6 
cubic  feet  per  minute.  The  actual  air-consumption  will  be 
somewhat  less  on  account  of  loss  of  pressure  in  the  valves  and 
passages;  it  may  be  fair  to  assume  160  cubic  feet  per  minute  for 
the  actual  consumption. 

In  order  to  make  one  complete  calculation  for  the  use  of  com- 
pressed air  for  transmitting  power,  the  data  for  the  compressed- 
air  engine  have  been  made  to  correspond  with  the  results  of  calcu- 
lations for  an  air-compressor  on  page  377  and  for  the  loss  of 
pressure  in  a  pipe  on  page  384.  Since  there  is  a  loss  of  pressure 
in  flowing  through  the  pipe  at  constant  temperature,  there  is 
a  corresponding  increase  of  volume,  so  that  the  pipe  delivers 

300  X  114.7  -*-  106.7  =  322-6 

cubic  feet  per  minute.     Our  calculation  for  the  air-consumption 
of  an  engine  to  deliver  100  horse-power  gives  about  160  cubic 
feet,  from  which  it  appears  that  the  system  of  compressor,  con- 
ducting-pipe,  and  compressed-air  engine  should  deliver 
100  X  322.6  -j-  1 60  =  200  -f  horse-power. 

If  the  friction  of  the  compressed-air  engine  is  assumed  to  be 
ten  per  cent,  the  power  delivered  by  it  to  the  main  shaft  (or  to 
the  machine,  driven  directly  from  it)  will  be 

200  X  .9  =  1 80  horse-power. 

The  steam-power  required  to  drive  a  simple  compressor  was 
found  to  be  520  horse-power;  it  consequently  appears  that 

1 80  -5-  520  =  0.34 
of  the  indicated  steam-power  is  actually  obtained  for  doing  work 


EFFICIENCY    OF  COMPRESSED-AIR  TRANSMISSION        391 

from  the  entire  system  of  transmitting  power.  If,  however,  a 
compound  compressor  is  used,  then  the  indicated  steam-power 
is  444,  and  of  this 

1 80  -5-  444  =  0.40 

will  be  obtained  for  doing  work. 

If,  however,  we  consider  that  the  power  would  in  any  case  be 
developed  in  a  steam-engine,  and  that  the  transmission  system 
should  properly  include  only  the  compressor-cylinder,  the  pipe, 
and  the  compressed-air  engine,  then  our  basis  of  comparison  will 
be  the  indicated  power  of  the  compressor-cylinder.  For  the 
simple  compressor  we  found  the  horse-power  to  be  442,  which 
gives  for  the  efficiency  of  transmission 

180  -f-  442  =  0.41, 

while  the  compound  compressor  demanded  only  377  horse- 
power, giving  an  efficiency  of 

1 80  •*-  377  =  0.48. 

It  appeared  that  the  failure  to  obtain  complete  compression 
involved  a  loss  of  about  13  per  cent  in  the  air-consumption. 
It  may  then  be  assumed  that  with  complete  compression  our 
engine  could  deliver  200  horse-power  to  the  main  shaft.  In 
that  case  the  efficiency  of  transmission  when  a  compound  com- 
pressor is  used  may  be  0.53. 

Efficiency  of  Compressed-air  Transmission.  —  The  preced- 
ing calculation  exhibits  the  defect  of  compressed  air  as  a  means 
of  transmitting  power.  It  is  possible  that  somewhat  better 
results  may  be  obtained  by  a  better  choice  of  pressures  or  pro- 
portions. Professor  Unwin  estimates  that  when  used  on  a  large 
scale  from  0.44  to  0.51  of  the  indicated  steam-power  may  be 
realized  on  the  main  shaft  of  the  compressed-air  engine.  On 
the  other  hand,  when  compressed  air  is  used  in  small  motors, 
and  especially  in  rock-drills  and  other  mining- machinery,  much 
less  efficiency  may  be  expected. 

Experiments  made  by  M.  Graillot  *  of  the  Blanzy  mines 
showed  an  efficiency  of  from  22  to  32  per  cent.  Experiments 

*  Pernolet,  UAir  Comprime,  pp.  549,  550. 


392  COMPRESSED   AIR 

made  by  Mr.  Daniel  at  Leeds  gave  an  efficiency  varying  from 
0.255  to  °-455>  with  pressures  varying  from  2.75  atmospheres 
to  1.33  atmospheres.  An  experiment  made  by  Mr.  Kraft*  gave 
an  efficiency  of  0.137  f°r  a  small  machine,  using  air  at  a  pressure 
of  five  atmospheres  without  expansion. 

Compressed  air  has  been  used  for  transmitting  power  either 
where  power  for  compression  is  cheap  and  abundant,  or  where 
there  are  reasons  why  it  is  specially  desirable,  as  in  mining  and 
tunnelling.  It  is  now  used  to  a  considerable  extent  for  driving 
hand-tools,  such  as  drills,  chipping-chisels,  and  calking-tools, 
in  machine-  and  boiler-shops,  and  in  shipyards.  It  is  also  used 
for  operating  cranes  and  other  machines  where  power  is  used 
only  at  intervals,  so  that  the  condensation  of  steam  (when  used 
directly)  is  excessive,  and  where  hydraulic  power  is  liable  to  give 
trouble  from  freezing. 

Compressed  air  has  been  used  to  a  very  considerable  extent 
for  transmitting  power  in  Paris.  The  system  appears  to  be 
expensive  and  to  be  used  mainly  on  account  of  its  convenience 
for  delivering  small  powers  or  in  places  where  the  cold  exhaust 
can  be  used  for  refrigeration.  The  trouble  from  freezing  of 
moisture  in  the  cylinder  has  been  avoided  by  allowing  the  air 
to  flow  through  a  coil  of  pipe  which  is  heated  externally  by  a 
charcoal  fire.  Professor  Unwin  estimates  that  an  efficiency  of 
transmission  of  0.75  may  be  attained  under  favorable  conditions 
when  the  air  is  heated  near  the  compressor,  but  he  does  not 
include  the  cost  of  fuel  for  reheating  in  this  estimate. 

Storage  of  Power  by  Compressed  Air.  —  Reservoirs  or  cylin- 
ders charged  with  compressed  air  have  been  used  to  store  power 
for  driving  street-cars.  A  system  developed  by  Mekarski  uses 
air  at  350  to  450  pounds  per  square  inch  in  reservoirs  having  a 
capacity  of  75  cubic  feet.  The  car  also  carries  a  tank  of  hot 
water  at  a  temperature  of  about  350°  F.,  through  which  the  air 
passes  on  the  way  to  the  motor  and  by  which  it  is  heated  and 
charged  with  steam.  This  use  of  hot  water  gives  a  secondary 
method  of  storing  power,  and  also  avoids  trouble  from  freezing 

*  Revue  universelle  des  Mines,  2  serie,  tome  vi. 


STORAGE    OF    POWER   BY   COMPRESSED   AIR  393 

in  the  motor-cylinders.  Air  at  much  higher  pressures  has  been 
used  for  driving  street-cars  in  New  York  City,  but  the  particu- 
lars have  not  been  given  to  the  public. 

The  calculation  for  storage  of  power  may  be  made  in  much 
the  same  way  as  that  for  the  transmission  of  power;  the  chief 
difference  is  due  to  the  fact  that  the  air  is  reduced  in  pressure 
by  passing  it  through  a  reducing-valve  on  the  way  from  the 
reservoir  to  the  motor.  By  the  theory  of  perfect  gases  such 
a  reduction  of  pressure  should  not  cause  any  change  of  tem- 
perature, but  the  experiments  of  Joule  and  Thomson  (page  69) 
show  that  there  will  be  an  appreciable,  though  not  an  important, 
loss  of  temperature  when  there  is  a  large  reduction  of  pressure. 
Thus  at  70°  F.  or  2i°.i  C.  the  loss  of  temperature  for  each  100 
inches  of  mercury  will  be 

•0°.92  X  /^V=  o°.79  C.  =  ii°  F. 
\294/ 

Now  100  inches  of  mercury  are  equivalent  to  about  49  pounds 
to  the  square  inch,  so  that  100  pounds  difference  of  pressure  will 
give  about  3^°  F.  reduction  of  temperature,  and  1000  pounds 
difference  of  pressure  will  give  about  35°  F.  reduction  of  tem- 
perature. The  last  figures  are  far  beyond  the  limits  of  the 
experiments,  and  the  results  are  therefore  crude.  Again,  the  air 
in  passing  through  the  reducing-valve  and  the  piping  beyond 
will  gain  heat  and  consequently  show  a  smaller  reduction  of  tem- 
perature. The  whole  subject  of  loss  of  temperature  due  to 
throttling  is  uncertain,  and  need  not  be  considered  in  practical 
calculations  for  air-compressors. 

For  an  example  of  the  calculation  for  storage  of  power  let  us 
find  the  work  required  to  store  air  at  450  pounds  per  square 
inch  in  a  reservoir  containing  75  cubic  feet.  Replacing  the 
specific  volume  vl  in  equation  (213)  by  the  actual  volume,  we 
have  for  the  work  of  compression  (not  allowing  for  losses  and 
imperfections) 


W  =  3  X  464-7  X  144  X  7S-_  _ 

I.4    —     I       (   \   14.7 

=  20520000  foot-pounds. 


394  COMPRESSED   AIR 

If  the  pressure  is  reduced  to  50  pounds  by  the  gauge  before  it  is 
used,  the  volume  of  air  will  be 

75  X  464.7  -r-  64.7  =  539  cubic  feet. 

The  work  for  complete  expansion  of  one  pound  to  the  pressure 
of  the  atmosphere  will  be 


and  the  work  for  539  cubic  feet  will  be 


7^-7  \  i  -  (g* 


144  X  64.7  X  539  7-7     i  -  $  =  S976ooo 

foot-pounds,  without  allowing  for  losses  or  imperfections.     The 
maximum  efficiency   of   storing  and    restoring  energy   by   the 
use  of  compressed  air  in  this  case  is  therefore 
5976000  -T-  20520000  =  0.29. 

In  practice  the  efficiency  cannot  be  more  than  0.25,  if  indeed 
it  is  so  high. 

Sudden  Compression.  —  It  may  not  be  out  of  place  to  call  atten- 
tion to  a  danger  that  may  arise  if  air  at  high  pressure  is  suddenly 
let  into  a  pipe  which  has  oil  mingled  with  the  air  in  it  or  even 
adhering  to  the  side  of  the  pipe.  The  air  in  the  pipe  will  be  com- 
pressed, and  its  temperature  may  become  high  enough  to  ignite  the 
oil  and  cause  an  explosion.  That  this  danger  is  not  imaginary  is 
shown  by  an  explosion  which  occurred  under  such  conditions  in 
a  pipe  which  was  strong  enough  to  withstand  the  air-pressure. 

Liquid  Air.  —  The  most  practical  way  of  liquefying  air  on  a 
large  scale  is  that  devised  by  Linde  depending  on  the  reduction 
of  the  temperature  by  throttling.  On  page  69,  is  given  the 
empirical  expression  deduced  by  Joule  and  Kelvin  for  the 
reduction  in  temperature  of  air  flowing  through  a  porous  plug 
with  a  difference  of  pressure  measured  by  100  inches  of  mercury, 

0.92 


LIQUID  AIR  395 

in  which  2  73°.  7  C.  is  taken  to  be  the  absolute  temperature  of 
freezing,  and  T  is  the  absolute  temperature  of  the  air. 

A  modern  three-stage  air-compressor  can  readily  give  a  press- 
ure of  2000  pounds  per  square  inch,  and  if  the  above  expression 
is  assumed  to  hold  approximately  for  such  a  reduction  in  pressure, 
it  indicates  a  cooling  of 


2000 


0.92  X ^^ =  37°.5  C. 

100  X  0.491 

or  about  67°  F.  By  a  cumulative  effect  to  be  described,  the  air 
may  be  cooled  progressively  till  it  reaches  the  boiling-point  of  its 
liquid  and  then  liquefied.  Linde's  liquefying  apparatus  consists 
essentially  of  an  air-compressor,  a  throttling-orifice,  and  a  heat 
interchange  apparatus. 

The  air-compressor  should  be  a  good  three-stage  machine 
giving  a  high  pressure.  The  throttling-orifice  may  be  a  small 
hole  in  a  metallic  plate.  The  heat  interchange  apparatus  may 
be  made  up  of  a  double  tube  about  400  feet  long,  the  inner  tube 
having  a  diameter  of  0.16  and  the  outer  tube  a  diameter  of  0.4 
of  an  inch ;  these  tubes  for  convenience  are  coiled  and  are  then 
thoroughly  insulated  from  heat.  The  air  from  the  compressor 
is  passed  through  the  inner  tube  to  the  throttle-orifice  and  then 
from  the  reservoir  below  the  orifice,  through  the  space  between 
the  inner  and  outer  tubes  back  to  the  compressor.  The  cumu- 
lative effect  of  this  action  brings  the  air  to  the  critical  temper- 
ature in  a  comparatively  short  period,  and  then  liquid  air  begins 
to  accumulate  in  the  reservoir  below  the  orifice,  whence  it  may  be 
drawn  off. 

The  atmospheric  air  before  it  is  supplied  to  the  condenser 
should  be  freed  from  carbon  dioxide  and  moisture,  which  would 
interfere  with  the  action,  and  should  be  cooled  by  passing  it 
through  pipes  cooled  with  water  and  by  a  freezing  mixture. 
The  portion  of  air  liquefied  must  be  made  up  by  drawing  air  from 
the  atmosphere,  which  is,  of  course,  purified  and  cooled. 

The  principal  use  of  liquid  air  is  the  commercial  production  of 
oxygen  by  fractional  distillation ;  several  plants  have  been  installed 
for  this  purpose. 


CHAPTER    XVI. 

REFRIGERATING-MACHINES. 

A  REFRIGERATING- MACHINE  is  a  device  for  producing  low 
temperatures  or  for  cooling  some  substance  or  space.  It  may 
be  used  for  making  ice  or  for  maintaining  a  low  temperature  in 
a  cellar  or  storehouse. 

Refrigeration  on  a  small  scale  may  be  obtained  by  the  solu- 
tion of  certain  salts;  a  familiar  illustration  is  the  solution  of 
common  salt  with  ice,  another  is  the  solution  of  sal  ammoniac 
in  water.  Certain  refrigerating- machines  depend  on  the  rapid 
absorption  of  some  volatile  liquid,  for  example,  of  ammonia  by 
water;  if  the  machine  is  to  work  continuously  there  must  be  some 
arrangement  for  redistilling  the  liquid  from  the  absorbent.  The 
most  recent  and  powerful  refrigerating- machines  are  reversed 
heat-engines.  They  withdraw  the  working  substance  (air  or 
ammonia)  from  the  cold-room  or  cooling-coil,  compress  it,  and 
deliver  it  to  a  cooler  or  condenser.  Thus  they  take  heat  from  a 
cold  substance,  do  work  arid  add  heat,  and  finally  reject  the  sum 
of  the  heat  drawn  in  and  the  heat  equivalent  of  the  work  done. 
These  reversed  heat-engines,  however,  are  very  far  from  being 
reversible  engines,  not  only  on  account  of  imperfections  and  losses 
but  because  they  work  on  a  non-reversible  cycle. 

Two  forms  of  refrigerating- machines  are  in  common  use,  air 
refrigerating- machines  and  ammonia  refrigerating- machines. 
Sometimes  sulphur  dioxide  or  some  other  volatile  fluid  is  used 
instead  of  ammonia.  Carbon  dioxide  has  been  used,  but  there  are 
difficulties  due  to  high  pressure  and  the  fact  that  the  critical  tem- 
perature is  88°  F. 

Air  Refrigerating-Machine.  —  The  general  arrangement  of 
an  air  refrigerating- machine  is  shown  by  Fig.  86.  It  consists 

396 


AIR   REFRIGERATING-MACHINE 


397 


of  a  compression-cylinder  A,  an  expansion-cylinder  B  of  smaller 
size,  and  a  cooler  C.  It  is  commonly  used  to  keep  the  atmos- 
phere in  a  cold-storage  room  at  a  low  temperature,  and  has 
certain  advantages  for  this  purpose,  especially  on  shipboard. 
The  air  from  the  storage-room  comes  to  the  compressor  at  or 
about  freezing-point,  is  compressed  to  two  or  three  atmospheres 
and  delivered  to  the  cooler,  which  has  the  same  form  as  a  sur- 
face-condenser, with  cooling  water  entering  at  e  and  leaving  at  /. 
The  diaphragm  mn  is  intended  to  improve  the  circulation  of 
the  cooling  water.  From  the  cooler  the  air,  usually  somewhat 
warmer  than  the  atmosphere,  goes  to  the  expansion-cylinder  B, 


Fro.  86. 

in  which  it  is  expanded  nearly  to  the  pressure  of  the  air  and 
cooled  to  a  low  temperature,  and  then  delivered  to  the  storage- 
room.  The  inlet-valves  a,  a  and  the  delivery-valves  b,  b  of 
the  compressor  are  moved  by  the  air  itself;  the  ad  mission- valves 
c,  c  and  the  exhaust-valves  d,  d  of  the  expansion-cylinder  are 
like  those  of  a  steam-engine  and  must  be  moved  by  the  machine. 
The  difference  between  the  work  done  on  the  air  in  the  com- 
pressor and  that  done  by  the  air  in  the  expansion-cylinder, 
together  with  the  friction  work  of  the  whole  machine,  must  be 
supplied  by  a  steam-engine  or  other  motor. 

It  is  customary  to  provide  the  compression-cylinder  with  a 
water-jacket  to  prevent  overheating,  and  frequently  a  spray 
of  water  is  thrown  into  the  cylinder  to  reduce  the  heating  and 
the  work  of  compression.  Sometimes  the  cooler  C,  Fig.  86, 


298  REFRIGERATING   MACHINES 

is  replaced  by  an  apparatus  resembling  a  steam-engine  jet-con- 
denser, in  which  the  air  is  cooled  by  a  spray  of  water.  In  any 
case  it  is  essential  that  the  moisture  in  the  air,  as  well  as  the 
water  injected,  should  be  efficiently  removed  before  the  air  is 
delivered  to  the  expansion-cylinder;  otherwise  snow  will  form 
in  that  cylinder  and  interfere  with  the  action  of  the  machine. 
Various  mechanical  devices  have  been  used  to  collect  and  remove 
water  from  the  air,  but  air  may  be  saturated  with  moisture  after 
it  has  passed  such  a  device.  The  Bell-Coleman  Company  use 
a  jet-cooler  with  provision  for  collecting  and  withdrawing  water, 
and  then  pass  the  air  through  pipes  in  the  cold-room  on  the 
way  to  the  expansion-cylinder.  The  cold-room  is  maintained 
at  a  temperature  a  little  above  freezing-point,  so  that  the  mois- 
ture in  the  air  is  condensed  upon  the  sides  of  the  pipes  and 
drains  back  into  the  cooler. 

When  an  air  refrigerating- machine  is  used  as  described,  the 
pressure  in  the  cold-room  is  necessarily  that  of  the  atmosphere, 
and  the  size  of  the  machine  is  large  as  compared  with  its  per- 
formance. The  performance  may  be  increased  by  running 
the  machine  on  a  closed  cycle  with  higher  pressures;  for  examplej 
the  cold  air  may  be  delivered  to  a  coil  of  pipe  in  a  non-freezing 
salt  solution,  from  which  the  air  abstracts  heat  through  the 
walls  of  the  pipe  and  then  passes  to  the  compressor  to  be  used 
over  again.  The  machine  may  then  be  used  to  produce  ice,  or 
the  brine  may  be  used  for  cooling  spaces  or  liquids.  A  machine 
has  been  used  for  producing  ice  on  a  small  scale,  without  cooling 
water,  on  the  reverse  of  this  principle;  that  is,  atmospheric  air 
is  first  expanded  and  chilled  and  delivered  to  a  coil  of  pipe  in 
a  salt  solution,  then  the  air  is  drawn  from  this  coil,  after  absorb- 
ing heat  from  the  brine,  compressed  to  atmospheric  pressure, 
and  expelled. 

Proportions  of  Air  Refrigerating-Machines.  —  The  perfor- 
mance of  a  refrigerating- machine  may  be  stated  in  terms 
of  the  number  of  thermal  units  withdrawn  in  a  unit  of  time, 
or  in  terms  of  the  weight  of  ice  produced.  The  latent  heat  of 
fusion  of  ice  may  be  taken  to  be  80  calories  or  144  B.T.U. 


PROPORTION   OF   AIR   OF   REFRIGERATING-MACHINES    399 

Let  the  pressure  at  which  the  air  enters  the  compression- 
cylinder  be  pv  that  at  which  it  leaves  be  p^  let  the  pressure  at 
cut-off  in  the  expanding-cylinder  be  ps  and  that  of  the  back- 
pressure in  the  same  be  p^  let  the  temperatures  correspond- 
ing to  these  pressures  be  tv  /2,  /3,  and  /4,  or,  reckoned  from  the 
absolute  zero,  Tv  Tv  Ty  and  T4.  With  proper  valve-gear 
and  large,  short  pipes  communicating  with  the  cold-chamber 
pt  may  be  assumed  to  be  equal  to  pl  and  equal  to  the  pressure 
in  that  chamber.  Also  /t  may  be  assumed  to  be  the  tempera- 
ture maintained  in  the  cold-chamber,  and  t3  may  be  taken  to 
be  the  temperature  of  the  air  leaving  the  cooler.  With  a  good 
cut-off  mechanism  and  large  passages  p3  may  be  assumed  to 
be  nearly  the  same  as  that  of  the  air  supplied  to  the  expanding- 
cylinder.  Owing  to  the  resistance  to  the  passage  of  the  air 
through  the  cooler  and  the  connecting  pipes  and  passages,  p3 
is  considerably  less  than  pr 

It  is  essential  for  best  action  of  the  machine  that  the  expan- 
sion and  compression  of  the  expanding-cylinder  shall  be  complete. 
The  compression  may  be  made  complete  by  setting  the  exhaust- 
valve  so  that  the  compression  shall  raise  the  pressure  in  the 
clearance-space  to  the  admission-pressure  ps  at  the  instant 
when  the  admission- valve  opens.  The  expansion  can  be  made 
complete  only  by  giving  correct  proportions  to  the  expanding- 
and  compression-cylinders. 

The  expansion  in  the  expanding-cylinder  may  be  assumed 
to  be  adiabatic,  so  that 


v  (23I) 

Were  the  compression  also  adiabatic  the  temperature  t2  could 
be  determined  in  a  similar  manner;  but  the 

n 

air  is  usually  cooled  during  compression, 
and  contains  more  or  less  vapor,  so  that  the 
temperature  at  the  end  of  compression  cannot 


FIG.  87.  De  determined  from  the  pressure  alone,  even 

though  the  equation  of  the  compression  curve  be  known. 


400  REFRIGERATING  MACHINES 

Let  the  air  passing  through  the  refrigerating-  machine  per 

minute  be  M\  then  the  heat  withdrawn  from  the  cold-room  is 

Qt  =  Mcp  (/,  -  «,)  ......  (232) 

The  work  of  compressing  M  pounds  of  air  from  the  pressure  pl 
to  the  pressure  p2  in  a  compressor  without  clearance  is  (Fig.  87) 


Wc  =  M      p,vz  +          pdv  - 


j*[(*  •-,]  ,4 


n  —  l 


(233) 


provided  that  the  compression  curve  can  be  represented  by  an 
exponential  equation.  If  the  compression  can  be  assumed  to 
be  adiabatic, 


<,-«,);    (234) 

—     * 

for  in  such  case  we  have  the  equations 


If  the  expansion  is  complete  in  the  expanding-cylinder,  as 
should  always  be  the  case,  then  the  equation  for  the  work  done 
by  the  air  will  have  the  same  form  as  equation  (233)  or  (234), 
replacing  tl  and  p  by  /4  and  p^  and  t2  and  p2  by  /3  and  p3 ;  so  that 

n  —  I 

n      (  fp^\   n  ) 

4  n  —  i  I  \pt  I  ) 

and  for  adiabatic  expansion 

w,  =  ^  (i,  -  O (236) 


PROPORTION    OF   AIR    OF    REFRIGERATING-MACHINES     401 

The  difference  between  the  works  of  compression  and  expan- 
sion is  the  net  work  required  for  producing  refrigeration;  conse- 
quently 

Me 
W=W,-W.=  ^\t,-tt-tt+t<\      .(237) 

or,  replacing  M  by  its  value  from  equation  (232), 


The  net  horse-power  required  to  abstract  Ql  thermal  units 
per  minute  is  consequently 


p 


33000          tt—tt 

where  tl  is  the  temperature  of  the  air  drawn  into  the  compressor, 
and  /2  is  the  temperature  of  the  air  forced  by  the  compressor  into 
the  cooler,  and  /3  is  the  temperature  of  the  air  supplied  to  the 
expanding*cylinder,  and  /4  is  the  temperature  of  the  cold  air 
leaving  the  expanding-cylinder.  The  gross  horse-power  devel- 
oped in  the  steam-engine  which  drives  the  refrigerating-  machine 
is  likely  to  be  half  again  as  much  as  the  net  horse-power  or  even 
larger.  The  relation  of  the  gross  and  the  net  horse-powers  for 
any  air  refrigerating-  machine  may  readily  be  obtained  by  indi- 
cating the  steam-  and  air-cylinders  and  may  serve  as  a  basis  for 
calculating  other  machines. 

The  heat  carried  away  by  the  cooling  water  is 

Q2  =  Q,  +  AW  .......    (240) 

If  compression  and  expansion  are  adiabatic,  then 
Q2  =  Mcp  (t,  -  /4  +  /,  4-  /4  -  /!  -  /,)  -  Mcp  (/,  -  /,)     .  (241) 
or,  replacing  M  by  its  value  from  equation  (232), 

......  (242) 

If  the  initial  and  final  temperatures  of  the  cooling  water  are 


402  REFRIGERATING    MACHINES 

/,  and  /*,  and  if  qt  and  qk  are  the  corresponding  heats  of  the 
liquid,  then  the  weight  of  cooling  water  per  minute  is 


The  compressor-cylinder  must  draw  in  M  pounds  of  air  per 
minute  at  the  pressure  pl  and  the  temperature  tlt  that  is,  with 
the  specific  volume  v^  consequently  its  apparent  piston  dis- 
placement without  clearance  will  be  at  N  revolutions  per  minute, 

Mv,      MRT,  (       . 

.....  (244) 


for  the  characteristic  equation  gives 

#!»•   =    R 

Replacing  M  by  its  value  from  equation  (232),  we  have 


=    RTl- 


. 
2NcpPl  (,,  -  ,4)       '     '     '     *(245) 

Since  all  the  air  delivered  by  the  compressor  must  pass  through 
the  expanding-cylinder,  its  apparent  piston  displacement  will  be 


(246) 


If  pv  the  pressure  of  the  air  entering  the  compression-cylinder 
is  equal  to  p^  that  of  the  air  leaving  the  expanding-cylinder  (as 
may  be  nearly  true  with  large  and  direct  pipes  for  carrying  the 
air  to  and  from  the  cold-room),  equation  (246),  will  reduce  to 

De  =  Dc  Ji    .......  (247) 

1   1 

Both  the  compressor-  and  the  expanding-cylinder  will  have 
a  clearance,  that  of  the  expanding-cylinder  being  the  larger. 
As  is  shown  on  page  363,  the  piston  displacement  for  an  air- 
compressor  with  a  clearance  may  be  obtained  by  dividing  the 
apparent  piston  displacement  by  the  factor 


CALCULATION   FOR   AN   AIR-REFRIGERATING   MACHINE  403 

If  the  expansion  and  compression  of  the  expanding-cylinder  are 
complete,  the  same  factor  may  be  applied  to  it.  For  a  refriger- 
ating-machine  n  may  be  replaced  by  tc  for  both  cylinders.  To 
allow  for  losses  of  pressure  and  for  imperfect  valve  action  the 
piston  displacements  for  both  compressor-  and  expanding- 
cylinders  must  be  increased  by  an  amount  which  must  be  deter- 
mined by  practice;  five  or  ten  per  cent  increase  in  volume  will 
probably  suffice.  In  practice  the  expansion  in  the  expanding- 
cylinder  is  seldom  complete.  A  little  deficiency  at  this  part 
of  the  diagram  will  not  have  a  large  effect  on  the  capacity  of 
the  machine,  and  will  prevent  the  formation  of  a  loop  in  the 
indicator-diagram;  but  a  large  drop  at  the  release  of  the  expand- 
ing-cylinder will  diminish  both  the  capacity  and  the  efficiency 
of  the  machine. 

The  temperature  /4  and  the  capacity  of  the  machine  may  be 
controlled  by  varying  the  cut-off  of  the  expanding-cylinder.  If 
the  cut-off  is  shortened  the  pressure  p2  will  be  increased,  and 
consequently  T^  will  be  diminished.  This  will  make  De,  the 
piston  displacement  of  the  expanding-cylinder,  smaller.  A 
machine  should  be  designed  with  the  proper  proportions  for  its 
full  capacity,  and  then,  when  running  at  reduced  capacity,  the 
expansion  in  the  expanding-cylinder  will  not  be  quite  complete. 

Calculation  for  an  Air-refrigerating  Machine.  —  Required 
the  dimensions  and  power  for  an  air  refrigerating- machine  to 
produce  an  effect  equal  to  the  melting  of  200  pounds  of  ice  per 
hour.  Let  the  pressure  in  the  cold-chamber  be  14.7  pounds  per 
square  inch  and  the  temperature  32°  F.  Let  the  pressure  of 
the  air  delivered  by  the  compressor-cylinder  be  39.4  pounds  by 
the  gauge  or  54.1  pounds  absolute,  and  let  there  be  ten  pounds 
loss  of  pressure  due  to  the  resistance  of  the  cooler  and  pipes  and 
passages  between  the  compressor-  and  the  expanding-cylinder. 
Let  the  initial  and  final  temperatures  of  the  cooling  water  be 
60°  F.  and  80°  F.,  and  let  the  temperature  of  the  air  coming 
from  the  cooler  be  90°  F.  Let  the  machine  make  60  revolutions 
per  minute. 

With  adiabatic  expansion  and  compression  the  temperatures 


404 


REFRIGERATING   MACHINES 


of  the  air  coming  from  the  compressor-  and  discharged  from  the 
expanding-cylinder  will  be 


0.4 

.  =    7*4; 

0.4 


T4  =  (460  +  90)    — =  402;  .'. 

\44.i/ 

The  melting  of  200  pounds  of  ice  is  equivalent  to 

200  X  144  -T-  60  =  480  B.T.U. 

per  minute;  consequently  the  net  horse-power  of  the  machine 
is  by  equation  (239) 


33000  /!    -    /4 

_  778  X  480       254  —  58  -  32  —  90 

33000  32    +   58 

=  778  X  480  X  74  =         H  p 

33000  X  90 

and  the  indicated  power  of  the  steam-engine  may  be  assumed 
to  be  14  horse-power. 

By  equation   (245)  the  apparent  piston  displacement  of  the 
compressor  without  clearance  will  be 


X  53-35  X  492  -   = 


2  X  60  X  0.2375  X  144  X  14.7  (32  +  58) 
By  equation   (247)  the  apparent  piston  displacement  of  the 
expanding-cylinder  without  clearance  will  be 

D.  =  Dcj±    •-=  2.33  X         -  =  1.90  cubic  feet. 


If  the  clearance  of  the  compressor-cylinder  is  0.02  of  its  piston 
displacement,  then  the  factor  for  clearance  by  equation  (191)  is 


_  =  o.979) 

mp          m  100  \i4.7          100 


COMPRESSION    REFRIGERATING-MACHINES 


405 


so  that  the  piston  displacement  becomes 

2.33  -r-  0.979  ==  2.38  cubic  feet. 

If,  further,  the  clearance  of  the  expander-cylinder  is  0.05  of 
its  piston  displacement,  the  factor  for  clearance  becomes 


100 
which  makes  the  piston  displacement 

1.90  -T-  0.963  =  1.97  cubic  feet. 

If  now  we  allow  ten  per  cent  for  imperfections,  we  will  get  for 
the  dimensions  :  stroke  2  feet,  diameter  of  the  compressor-cylinder 
15!  inches,  and  diameter  of  the  expanding-cylinder  14  inches. 

Compression  Refrigerating-Machine.  —  The  arrangement  of 
a  refrigerating-  machine  using  a  volatile  liquid  and  its  vapor  is 


FIG.  88. 

shown  by  Fig.  88.  The  essential  parts  are  the  compressor  A, 
the  condenser  B,  the  valve  J9,  and  the  vaporizer  C.  The  com- 
pressor draws  in  vapor  at  a  low  pressure  and  temperature, 
compresses  it,  and  delivers  it  to  the  condenser,  which  consists 
of  coils  of  pipe  surrounded  by  cooling  water  that  enters  at  e  and 
leaves  at  /.  The  vapor  is  condensed,  and  the  resulting  liquid 


4o6  REFRIGERATING  MACHINES 

gathers  in  a  reservoir  in  the  bottom,  from  whence  it  is  led  by  a 
small  pipe  having  a  regulating- valve  D  to  the  vaporizer  or 
refrigerator.  The  refrigerator  is  also  made  up  of  coils  of  pipe, 
in  which  the  volatile  liquid  vaporizes.  The  coils  may  be  used 
directly  for  cooling  spaces,  or  they  may  be  immersed  in  a  tank 
of  brine,  which  may  be  used  for  cooling  spaces  or  for  making  ice. 
Fig.  88  shows  the  compressor  with  one  single-acting  vertical 
cylinder  which  has  head-valves,  foot-valves,  and  valves  in  the 
piston.  Small  machines  usually  have  one  double-acting  com- 
pressor cylinder.  Large  machines  have  vertical  compressors 
which  may  be  single-acting  or  double  acting. 

The  cycle  which  has  been  stated  for  the  compression 
refrigerating- machine  is  incomplete,  because  the  working  fluid 
is  allowed  to  flow  through  the  expansion-cock  into  the  expanding- 
coils  without  doing  work.  To  make  the  cycle  complete,  there 
should  be  a  small  expanding-cylinder  in  which  the  liquid  could 
do  work  on  the  way  from  the  condenser  to  the  vaporizing-coils ; 
but  the  work  gained  in  such  a  cylinder  would  be  insignificant, 
and  it  would  lead  to  complications  and  difficulties. 

Proportions  of  Compression  Refrigerating-Machines.  —  The 
liquid  condensed  in  the  coils  of  the  condenser  flows  to  the  expan- 
sion-cock with  the  temperature  t1  and  has  in  it  the  heat  qr  In 
passing  through  the  expansion-cock  there  is  a  partial  vaporiza- 
tion, but  no  heat  is  gained  or  lost.  The  vapor  flowing  from  the 
expansion-coils  at  the  temperature  /2  and  the  pressure  p2  is 
usually  dry  and  saturated,  or  perhaps  slightly  superheated,  as  it 
approaches  the  compressor.  Each  pound  consequently  carries 
from  the  expanding-coils  the  total  heat  Hr  Consequently 
the  heat  withdrawn  from  the  expanding-coil  by  a  machine  using 
M  pounds  of  fluid  per  minute  is 

Ql  =  M  (H,  -  ?1) (246) 

The  compressor-cylinder  is  always  cooled  by  a  water-jacket, 
but  it  is  not  probable  that  such  a  jacket  has  much  effect  on  the 
working  substance,  which  enters  the  cylinder  dry  and  is  super- 
heated by  compression.  We  may  consequently  calculate  the 


PROPORTIONS   OF  COMPRESSION  407 

temperature  of  the  vapor  delivered  by  the  compressor  by  aid  of 
equation  (80),  page  65,  giving 


This  equation  may  be  used  because  it  is  equivalent  to  the 
assumption  with  regard  to  entropy  on  page  121.  The  value 
of  a  is  i  for  ammonia  and  0.22  for  sulphur  dioxide  as  given  on 
pages  119  and  124. 

As  has  already  been  pointed  out,  the  vapor  approaching  the 
compressor  may  be  treated  as  though  it  were  dry  and  saturated, 
each  pound  having  the  total  heat  Hr  The  vapor  discharged  by 
the  compressor  at  the  temperature  /,  and  the  pressure  pl  will 
have  the  heat 

CP  ft  -  O  +  Hr 

The  heat  added  to  each  pound  of  fluid  by  the  compressor  is 
consequently 

Cp  (ts  -  g  +  HI  -  HV 

and  an  approximate  calculation  of  the  horse-power  of  the  com- 
pressor may  be  made  by  the  equation 

778M  \ca  (t,  -  Q  +  H,  -  H,] 

33000  '   (250) 

or,  substituting  for  M  from  equation  (249), 

p      778Q.  \c.  p. -Q  +H,  -HJ 
33000  (H,  -  ?1) 

The  power  thus  calculated  must  be  multiplied  by  a  factor  to 
be  found  by  experiment  in  order  to  find  the  actual  power  of  the 
compressor.  Allowance  must  be  made  for  friction  to  find  the 
indicated  power  of  the  steam-engine  which  drives  the  motor;  for 
this  purpose  it  will  be  sufficient  to  add  ten  or  fifteen  per  cent  of 
the  power  of  the  compressor. 

The  heat  in  the  fluid  discharged  by  compressor  is  equal  to 
the  sum  of  the  heat  brought  from  the  vaporizing-coils  and  the 
heat-equivalent  of  the  work  of  the  compressor.  The  heat  that 


408  REFRIGERATING-MACHINES 

must  be  carried  away  by  the  cooling  water  per  minute  is  con- 
sequently 

Q2  =  M  (H2  -  qj  +  M\c,  (/,  -  /J  +  Hl  -  #2{; 
.'.    Qt  =  M\c,(t.-tJ  +  rj  .........  (252) 

where  rt  is  the  heat  of  vaporization  at  the  pressure  pr 

If  the  cooling  water  has  the  initial  temperature  4,  and  the  final 
temperature  t'WJ  and  if  qw  and  q'w  are  the  corresponding  heats  of 
the  liquid  for  water,  then  the  weight  of  cooling  water  used  per 
minute  will  be 


QW          y  w 

If  the  vapor  at  the  beginning  of  compression  can  be  assumed 
to  be  dry  and  saturated,  then  the  volume  of  the  piston  displace- 
ment of  a  compressor  without  clearance,  and  making  N  strokes 
per  minute,  is 

n     MVI 

D=-^f      .......  (254) 

To  allow  for  clearance,  the  volume  thus  found  may  be  divided 
by  the  factor 

m  \p2  1       m' 

as  is  explained  on  page  363.  The  volume  thus  found  is  further 
to  be  multiplied  by  a  factor  to  allow  for  inaccuracies  and 
imperfections. 

The  vapors  used  in  compression-machines  are  liable  to  be 
mingled  with  air  or  moisture,  and  in  such  case  the  performance 
of  the  machine  is  impaired.  To  allow  for  such  action  the  size 
and  power  of  the  machine  must  be  increased  in  practice  above 
those  given  by  calculation.  Proper  precautions  ought  to  be 
taken  to  prevent  such  action  from  becoming  of  importance. 

Calculation  for  a  Compression  Refrigerating-Machine.  —  Let 
it  be  required  to  find  the  dimensions  and  power  for  an  ammonia 
refrigerating-  machine  to  produce  2000  pounds  of  ice  per  hour 
from  water  at  80°  F.  Let  the  temperature  of  the  brine  in  the 


FLUIDS   AVAILABLE  409 

freezing-  tank  be  i5°F.,  and  the  temperature  in  the  condenser 
be  85°  F.  Assume  that  the  machine  will  have  one  double- 
acting  compressor,  and  that  it  will  make  80  revolutions  per 
minute. 

The  heat  of  the  liquid  for  water  at  80°  F.  is  48  B.T.U.,  and  the 
heat  of  liquefaction  of  ice  is  144,  so  that  the  heat  which  must 
be  withdrawn  to  cool  and  freeze  one  pound  of  water  will  be 
48  +  144  =  192  B.T.U. 

If  we  allow  50  per  cent  loss  for  radiation,  conduction,  and 
melting  the  ice  from  the  freezing-cans,  the  heat  which  the  machine 
must  withdraw  for  each  pound  of  ice  will  be  about  300  B.T.U.  ; 
consequently  the  capacity  of  the  machine  will  be 

Q±  =  2000  X  300  -T-  60  =  10000  B.T.U.  per  minute. 
The  pressures  for  ammonia  corresponding  to  15°  and  85°  F., 
are  42.43  and  165.47  pounds  absolute  per  square  inch,  so  that  by 
equation  (249) 

-(.5  +  460, 

/.     /,  =  668  -  460  =  208°  F. 
The  horse-power  of  the  compressor  is 

778Q,  {c,(<.  -Q  +g,  - 


33000  (H2  -  qj 
^778  X  loooo  £0.50836  (208-85)  +  SS6  -  535  j 

33ooo  (535  -  58) 

If  we  allow  10  per  cent  for  imperfections,  the  compressor  will 
require  45  horse-power.  If,  further,  15  per  cent  is  allowed  for 
friction,  the  steam-engine  must  develop  53  horse-power. 

From  equation  (248)  the  weight  of  ammonia  used  per  minute 
is 
M  =  Ql  •*-  (JET,  -  QJ  =  10000  -5-  (535  -  58)  =  21  pounds; 

and  by  equation   (254)  the  piston  displacement  for  the  com- 
pressor will  be 


~  2     21  X  6.93  ,  .    r 

D  =  -TT72  =  --  —^-°  =  o.o  i  cubic  feet. 
N         2  X  So 


4io 


REFRIGERATING-MACHINES 


If  10  per  cent  is  allowed  for  clearance  and  imperfect  valve 
action,  the  piston  displacement  will  be  one  cubic  foot,  and  the 
diameter  may  be  made  ioj  inches  and  the  stroke  20  inches. 

Fluids  Available.  —  The  fluids  that  have  been  used  in  compres- 
sion refrigerating- machines  are  ether,  sulphur  dioxide,  ammonia, 
and  a  mixture  of  sulphur  dioxide  and  carbon  dioxide,  known  as 
Pictet's  fluid.  The  pressures  of  the  vapors  of  these  fluids  at  sev- 
eral temperatures,  and  also  the  pressure  of  the  vapors  of  methylic 
ether  and  carbon  dioxide,  are  given  in  the  following  table: 

PRESSURES   OF  VAPORS,   MM.    OF  MERCURY. 


Temperatures 
Degrees 
Centigrade. 

Ether. 

Sulphur 
Dioxide. 

Methyl- 
Ether. 

Ammonia. 

Carbon 
Dioxide. 

Pictet's 
Fluid. 

~  3° 

287.5 

576.5 

866.1 

585 

—  2O 

68.9 

479-5 

882.0 

1392.1 

15142 

745 

—  IO 

114.7 

762.5 

1306.6 

2144.6 

20340 

1018 

0 

184.4 

1165.1 

1879.0 

3183.3 

26907 

i39i 

10 

286.8 

1719.6 

2629.0 

4574-0 

V  34999 

1938 

20 

432.8 

2462.1 

3586.0 

6387.8 

44717 

2584 

30 

634.8 

3431-8 

4778.0 

8701  .0 

56119 

3382 

40 

907.0 

4670.2 

"595-3 

69184 

4347 

Ether  was  used  in  the  early  compression-machines,  but  at  the 
temperatures  maintained  in  the  refrigerator  the  pressure  is 
small  and  the  specific  volume  large,  so  that  the  machines,  like 
air  refrigerating- machines,  were  either  feeble  or  bulky.  More- 
over, air  was  liable  to  leak  into  the  machine  and  unduly  heat  the 
compressor -cylinder.  Sulphur  dioxide  has  been  used  success- 
fully, but  it  has  the  disadvantage  that  sulphuric  acid  may  be 
formed  by  the  leakage  of  moisture  into  the  machine,  in*  which 
case  rapid  corrosion  occurs.  Ammonia  has  been  extensively 
used  in  the  more  recent  machines  with  good  results.  When 
distilled  from  an  aqueous  solution  it  is  liable  to  contain  con- 
siderable moisture.  As  is  shown  by  the  table,  Pictet's  fluid  has 
a  pressure  at  low  temperature  intermediate  between  the  pressures 
of  sulphur  dioxide  and  ammonia,  and  the  pressure  increases 
slowly  with  the  temperature.  It  has  been  used  by  the  inventor 


ABSORPTION    REFRIGERATING   APPARATUS 


411 


only,  and  does  not  appear  in  practice  to  have  any  advantage  over 
ammonia. 

Absorption  Refrigerating  Apparatus.  —  Fig.  89  gives  an 
ideal  diagram  of  a  continuous  absorption  refrigerating  appara- 
tus. It  consists  of  the  following  essential  parts:  (i)  the  gen- 
erator B,  containing  a  concentrated  solution  of  ammonia  in 
water,  from  which  the  ammonia  is  driven  by  heat;  (2)  the  con- 
denser C,  consisting  of  a  coil  of  pipe  in  a  tank,  through  which 
cold  water  is  circulated;  (3)  the  valve  F,  for  regulating  the 
pressures  in  C  and  in  /;  (4)  the  refrigerator  /,  consisting  of  a 
coil  of  pipe  in  a  tank  containing  a  non-freezing  salt  solution; 
(5)  the  absorber  A,  containing  a  dilute  solution  of  ammonia, 
in  which  the  vapor  of  ammonia  is  absorbed;  and  (6)  the  pump 
P  for  transferring  the  solution  from  the  bottom  of  A  to  the  top 
of  B;  there  is  also  a  pipe  connecting  the  bottom  of  B  with  the 
top  of  A.  It  is  apparent  that  the  condenser  and  refrigerator 
or  vaporizer  correspond  to  the  parts  B  and  C  of  Fig.  88,  and 
that  the  absorber  and  generator  take  the  place  of  the  compressor. 
The  pipes  connecting^  and  B  are  arranged  to  take  the  most 


FIG.  89. 

concentrated  solution  from  A  to  B,  and  to  return  the  solution 
from  which  the  ammonia  has  been  driven,  from  B  to  A.  In 
practice  the  generator  B  is  placed  over  a  furnace,  or  is  heated 
by  a  coil  of  steam-pipe,  to  drive  off  the  ammonia.  Also,  arrange- 
ments are  made  for  transferring  heat  from  the  hot  liquid  flow- 
ing from  B  to  A  to  the  cold  liquid  flowing  from  A  to  B.  As 


412 


REFRIGERATING-MACHINES 


the  ammonia  is  distilled  from  water  in  B  the  vapor  driven  off 
contains  some  moisture,  which  causes  an  unavoidable  loss  of 
efficiency. 

Tests  of  an  Air  Refrigerating-Machine.  —  An  air  refriger- 
ating-machine,  constructed  under  the  Bell-Coleman  patent, 
was  tested  by  Professor  Schroter  *  at  an  abattoir  in  Hamburg, 
where  it  was  used  to  maintain  a  low  temperature  in  a  storage- 
room.  The  machine  is  horizontal,  and  has  the  pistons  for  the 
expansion-  and  compression-cylinders  on  one  piston-rod,  the 
expansion-cylinder  being  nearer  the  crank.  Power  is  furnished 
by  a  steam-engine  acting  on  a  crank  at  the  other  end  of  the 
main  shaft  and  at  right  angles  to  the  crank  driving  the  air- 
pistons.  Both  the  steam-cylinder  and  the  expansion-cylinder 
have  distribution  slide-valves,  with  independent  cut-off  valves. 
The  main  dimensions  are  given  in  the  following  table: 

DIMENSIONS   BELL-COLEMAN  MACHINE. 


Steam- 
Cylinder. 

Compression- 
Cylinder. 

Expansion- 
Cylinder. 

Head 
End. 

Crank 
End. 

Head 
End. 

Crank 
End. 

Head 
End. 

Crank 
End. 

Diameter  of  piston,  cm  

53 
8.1 
0.605 
5-9 

53 
6.9 
0.605 
5-8 

7i 
9-° 
0.605 
1.4 

?i 
6.8 
0.605 
i-4 

53 
9.0 
0.605 
8  9 

53 
9.0 
0.605 
8.9 

Diameter  of  piston-rod,  cm  

Clearance,  percent  of  piston  displacement. 

Water  is  sprayed  into  the  compression-cylinder,  and  the  air 
is  further  cooled  by  passing  through  an  apparatus  resembling 
a  steam-engine  jet-condenser,  after  which  it  is  dried  by  passing 
it  through  a  system  of  pipes  in  the  cold-room  before  it  passes 
to  the  expansion-cylinder. 

In  the  tests,  indicators  were  attached  to  each  end  of  the  several 
cylinders,  and  the  temperature  of  the  air  was  taken  at  entrance 
to  and  exit  from  each  of  the  air-cylinders.  Specimens  of  the 
indicator-diagrams  from  the  air-cylinders  show  for  the  com- 
pressor a  slight  reduction  of  pressure  during  admission  and 
some  irregularity  during  expulsion,  and  for  the  expansion- 

*  Untersuchungen  an  Kaltemachinen ,  i88y. 


TESTS    OF  AN   AIR   REFRIGERATING-MACHINE 


413 


cylinder  a  little  wire-drawing  at  cut-off,  and  a  good  expansion 
and  compression,  though  neither  is  complete.  No  attempt 
was  made  to  measure  the  amount  and  temperatures  of  the  cool- 
ing water. 

The  data  and  results  of   the  tests  and  the  calculations  are 
given  in  Table  XXXVI. 

TABLE  XXXVI. 

TESTS   ON    BELL-COLEMAN   MACHINE. 


Number  of  test      

Duration  in  hours 

Revolutions  per  minute 

Temperatures  of  air,  degrees  Centigrade  : 

At  entrance  to  compression-cylinder 

At  exit  from  compression-cylinder 

At  entrance  to  expansion-cylinder 

At  exit  from  expansion- cylinder 

Mean  effective  pressure,  kgs.  per  sq.  cm.: 

Steam-cylinder :  head  end 

crank  end 

Compression-cylinder:  head  end 

crank  end 

Expansion-cylinder:  head  end 

crank  end 

Indicated  horse-power  : 

Steam-cylinder 

Compression-cylinder 

Expansion- cylinder 

Mean  pressure  during  expulsion  from  compression-cylinder,  kgs.  . 
Mean  pressure  during  admission  to  expansion-cylinder,  kgs.    .    .    . 

Difference 

Calculation  from  compression  diagram  : 

Absolute  pressure  at  end  of  stroke,  kgs 

Absolute  pressure  at  opening  of  admission- valve,  kg.: 

Head  end 

Crank  end 

Volume  at  admission,  per  cent  of  piston  displacement  : 

Head  end 

Crank  end 

Weight  of  air  discharged  per  stroke,  kg.: 

Head  end 

Crank  end 

Weight  of  air  discharged  per  revolution,  kg 

Calculation  from  expansion  diagram  : 
Absolute  pressure  at  release,  kgs.  : 

Head  end 

Crank  end 

Absolute  pressure  at  compression,  kgs.  : 

Head  end 

Crank  end 

Volume  at  release,  per  cent  of  piston  displacement: 

Head,  end 

Crank  end 

Volume  at  compression,  per  cent  of  piston  displacement : 

Head  end 

Crank  end 

Air  used  per  stroke,  kg.  : 

Head  end 

Crank  end 

Air  used  per  revolution 

Difference   of   weights,   calculated  by  compression  and  expansion 

diagrams,  kg 

In  per  cent  of  the  former 

Mean  weight  of  air  per  revolution,  kg 

Elevation  of  temperature  at  constant  pressure,  degrees  Centigrade. 
Heat  withdrawn  per  H.  P.  per  hour,  calories       


I. 
6 
65-05 

iQ-3 
27.3 
19.00 
—  47.0 

2.263 
2.239 
i  .900 
1.869 
1.592 
1.615 

85.12 

128.85 

60. 10 

3-35 

2.82 

0.53 

1.04 

0.783 
0.765 

6.15 
8.50 

0.2744 
0.2716 
0.546 


1.32 

1.45 

1.14 

1.20 
104.65 

106.1 

16.5 
19.8 

0.234 
0.254 
0.488 

0.058 
10.6 

0.514 
66.3 


II. 
1.63 
61.2 


26.8 
16.6 

—  47.0 

2.336 
2.294 
1.861 
1.825 
1.589 
1-594 

82.35 
"8.55 

56.12 
3-25 
2.83 
0.42 

1.04 

0.788 
0.749 

5-95 
8.41 

0.2764 
0.2742 
0-551 


1.31 

1.44 

1.14 
1.19 

104.7 
106.3 

16.0 
19.6 

0.233 
0.254 
0.487 

0.064 
ii. 6 

0.519 
64-5 

354 


III. 
2.92 

63.5 

19.1 

27.2 

19.1 

—  47.0 

2-343 
2.301 
1.870 
1.906 
1.626 
1.624 

85-71 
126.01 

59.46 
3-40 
2.84 
0.56 

1.04 

0.764 
0.765 

6.03 
7.91 

0.2750 
0.2730 
0.548 


1.17 

1.22 


104.8 


16.6 

20.6 

0.238 
0.255 
0.493 

0.055 

10.  O 

0.520 
66.1 
363 


TABLE  XXXVII. 

TESTS   ON   REFRIGERATING   MACHINES. 
BY  PROFESSOR  SCHROTER. 


Number. 

System  of  the  machine. 

Dimensions  of  the  steam 
cylinder. 

Dimensions  of  the 
compression  cylinder. 

Duration  of  test. 

Diameter  of 
piston,  mm. 

Diameter  of 
piston-rod, 
mm. 

a 

a 

Diameter  of 
piston,  mm. 

Diameter  of 
piston-rod, 
mm. 

i 

in 

i  

2   

Linde. 
Pictet. 

37i(-25 
400 

330 

450 

55;  5 

52 
68 

800 
602 

740 
900 

325 
250 

430 

6,? 
# 

ft 

540 
420 

900 

36  min. 
34 
106 
50   ' 
46-' 
35    ' 
3  hrs. 

8.5     " 
11.08" 
9.83 

4.00  " 

3  

5  

6  : 

7  .... 

8  :.: 

ig  

II  .. 

12  

Number. 

Revolutions  per  minute 
compressor. 

Indicated  horse-power 
of  steam  cylinder. 

Indicated  horse-power 
of  compressor. 

Absolute  pressures  of  vapor, 
kilos,  per  sq.  centimeter. 

Cooling  water. 

In  compressor 
during 
expulsion. 

In  condenser. 

i  i 

fe  tc'$ 

111 

&°* 

In  vaporizer. 

Initial 
temperature. 

\H 

i  

64.8 
59-8 

54-7 
55-1 
59-1 

53-6 
66.1 

45-9 
26.27 

27.30 
29.23 
24.49 

18.1 
25.8 
52.01 
61  .  70 
66.42 
75-02 

'9-'  58 

8.13 
10.68 
3-77 
4.11 
4-23 
5-8i 

6-99 
9-31 
13-66 

14.06 
14.11 
13-78 

7-87 
10.41 

3-22 
3-50 
3-62 

5-n 

2.50 

2.36 

2.97 

0-45 
0.63 
0.73 
0.67 

2.76 
2.64 
{4.851 
U-55J 
4-90) 
(4-53) 
4-91 
U.55) 
4-27  1 
4-83! 
2.63 
3-24 
0.82 
1-03 
I.  IS 
i.  06 

11.19 

II.  2 
II.  2 

ii.  i 

8.77 
8.82 
10.15 

10.  I 

10.15 
10.3 

22.56 

23.58 
23.04 

26.  10 

12.41 
20.45 
14.0 
15.95 
17.20 
3i-i 

3  
4  
5  
6 

7  ... 

65-15 
65.8 
64.2 
64-7 
64.5 
64.0 

26.1 
34-5 
91.  2 
94-5 
99-2 

I:  :: 

Q    

10   

IT   

12   

Number 

Ice  formed. 

Temperature  of 
water  or  brine 
cooled. 

as. 
!dJ 

q 

jS2 

Temperature  of 
water  supplied, 
degrees  C. 

Per  compressor 
horse-  power, 
per  hour, 
gross,  kilos. 

f*-25! 

SJ3&S 

OH 

< 

At  exit. 

i    ... 

9-0 
8.3 

34^8 

31-7 

—4.4 
—5-9 
n.  19 

II.  2 
II.  2 
II.  I 
—9-50 

=£, 

10.  0 

—  9-7 
—  6.05 

—4.4 
—  5-9 

2-95 
2.38 
2.24 
4.71 

—  9-97 

—  4-i 
—  18.2 
—  10.  o 
—  9-7 
—  6.05 

4444 
3120 

3249 
3367 
3072 

3263 

3684 
3086 
1674 
2385 
2638 
1958 

4   

g    

6      . 

Q 

"•3 
ii.  3 
n-3 
H-3 

16.8 
25.0 
28.2 

20.6 

.15-2 

22.6 
25-9 
l8.5 

10  

II 

12     

TESTS    OF    COMPRESSION-MACHINES  415 

Tests  of  Compression-Machines. — In  Table  XXXVII  are  given 
the  data  and  results  of  tests  on  three  refrigerating- machines 
on  the  Linde  system  using  ammonia,  and  of  a  machine  on 
Pictet's  system  using  Pictet's  fluid,  all  by  Professor  Schroter. 
The  tests  on  machines  used  for  making  ice  were  necessarily  of 
considerable  length,  but  the  tests  on  machines  used  for  cool- 
ing liquids  were  of  shorter  duration. 

The  cooling  water  when  measured  was  gauged  on  a  weir  or 
through  an  orifice.  In  the  tests  3  to  6  on  a  machine  used  for 
cooling  fresh  water  the  heat  withdrawn  was  determined  by 
taking  the  temperatures  of  the  water  cooled,  and  by  gauging 
the  flow  through  an  orifice,  for  which  the  coefficient  of  flow  was 
determined  by  direct  experiment.  The  heat  withdrawn  in 
the  tests  7  and  8  was  estimated  by  comparison  with  the  tests 
3  to  6.  The  net  production  of  ice  in  the  tests  i  and  2  was  deter- 
mined directly;  and  in  the  test  2  the  loss  from  melting  during 
the  removal  from  the  moulds  was  found  by  direct  experiment 
to  be  8.45  per  cent.  By  comparison  with  this  the  loss  by  melting 
in  the  first  test  was  estimated  to  be  7.7  per  cent.  The  gross 
production  of  ice  in  the  refrigerator  was  calculated  from  the 
net  production  by  aid  of  these  figures.  In  the  tests  9  to  12  on 
the  Pictet  machine  the  gross  production  was  determined  from 
the  weight  of  water  supplied,  and  the  net  production  from  the 
weight  of  ice  withdrawn. 

A  separate  experiment  on  the  machine  used  for  cooling  brine 
gave  the  following  results  for  the  distribution  of  power : 

Total  horse-power .  57.1 

Power  expended  on  compressor 19.5 

"          "   centrifugal  pump 9.8 

"   water-pump      3.6 

The  centrifugal  pump  was  used  for  circulating  the  brine 
through  a  system  of  pipes  used  for  cooling  a  cellar  of  a  brew- 
ery. The  water-pump  supplied  cooling  water  to  the  condenser 
and  for  other  purposes. 


4i  6 


REFRIGERATING-MACHINES 


A  similar  test  on  the  Pictet  machine  gave: 

Power  of  engine  alone 7.9  H.  P. 

"     "       "    and  intermediate  gear 16.6      li 

"     "        ll    gear,  and  pump .      20.0      ' ' 

In  1888  comparative  tests  were  made  by  Professor  Schroter, 
on  a  Linde  and  on  a  Pictet  refrigerating-machine,  in  a  special 
building  provided  by  the  Linde  Company  which  had  every 
convenience  and  facility  for  exact  work.  The  following  table 
gives  the  principal  dimensions  of  the  machines: 


PRINCIPAL   DIMENSIONS   OF   LINDE   AND   PICTET 
REFRIGERATING-MACHINES. 


Linde. 

Pictet. 

Diameter  of  steam-cylinder,  cm  
compressor-cylinder,  cm.    .            ... 

30-55 

2<    O3 

3I-63 
28  6 

steam  piston-rod,  cm  
compressor-rod   cm 

4.85 

r    r 

5 

Stroke  of  steam-piston,  cm. 

7O 

62 

compressor,  cm  
Diameter  of  pipe  in  vaporizers,  external,  mm.      .    .    . 
internal,  mm  
Length  of  pipe  in  first  vaporizer  m 

42 

40-5 
32 
er6    C 

62 

44 
36 
r-?g    2 

second  vaporizer,  m. 

ecS    X 

t->g    2 

Diameter  of  pipe  in  condenser,  external,  mm  
internal,  mm  
Length  of  pipe  in  condenser,  m  

38.5 

3° 
556-2 

44 
36 
483.1 

The  Linde  machine  used  ammonia  and  was  allowed  to  draw 
a  mixture  of  liquid  and  vapor  into  the  compressor,  so  that  no 
water-jacket  was  required.  The  Pictet  machine  used  Pictet's 
fluid,  which  is  a  mixture  of  sulphur  dioxide  and  carbon  dioxide 
and  had  the  compressor  cooled  by  a  water-jacket. 

The  data  and  results  of  the  tests  are  given  in  Table  XXXVIII. 
Five  tests  were  made  on  each  machine.  The  temperature  of 
the  salt  solution  or  brine,  from  which  heat  was  withdrawn  by  the 
vaporizers,  was  allowed  to  vary  about  three  degrees  centigrade 
from  entrance  to  exit.  The  entrance  temperatures  were  intended 


TESTS    OF   COMPRESSION-MACHINES 


417 


TABLE  XXXVIII. 

TESTS    ON   REFRIGERATING-MACHINES. 
By  Professor  M.  SCHROTER,  Vergleichende  Versuche  an  Kdltemaschinen. 


Pictet  machine. 

One  vaporizer. 

I 

II 

III 

IV 

V 

Steam-engine  : 

57-o 

21    8l 

16.82 

0.771 

3-99 
1.47 

6.10 
3-o8 
0.850 
6.09 
3-03 
6.  ii 
3  05 

9-65 
19  72 
IS-S 

9-57 
19.71 

9.67 
19.71 
+  0.6 

35°7 

56.8 
20.88 

16.  10 
0.771 

3-9i 

1-05 

-1.96 
—4.98 
0.847 

2.  O2 
4.99 
2.04 
—4.98 

9.OO 
19.70 

15-6 

9.64 
19.72 

9-57 
19.64 
+  0.6 

2556 

57-1 
i8.75 

14.  26 
0.761 

3  84 
0.68 
—  9.92 

12.  91 
0.845 
9-91 
12.91 

—  9-94 
—12.88 

9.61 
19-59 
16.8 

9.58 
19-37 

9.  61 
19-35 
+  0.4 

1852 

57-6 
15-93 

11-83 
0-743 

4-25 
0.17 

—17-93 
—  20.96 
0.841 
—18.00 

2  I  .  00 
18.00 
21.00 

9.68 
19-51 
16.7 

9.68 
19.52 

9.72 
19-59 

-i-3 

1075 

59-3 
27.56 

22.91 
0.831 

6-39 
1-05 

—2.04 
—  5-oi 
0.846 
—  1-99 
—  5-02 

—2.05 
—4.96 

9.68 
35.18 

18.6 

9-73 
35-oS 

9.72 
35-01 
+  8.9 

1702 

Indicated  horse-power   

Compressor  : 

Mechanical  efficiency             .        

Pressure  in.  condenser,  kilograms  per  square 
centimetre     
Pressure  in  vaporizer,  kilograms  per  square 

Vaporizer  : 
Mean  temperature  of  brine,  entrance     .    . 
Mean  temperature  of  brine,  exit      .... 
Specific  heat  per  litre     

Initial  temperature  of  brine,  entrance     .    . 

Final  temperature  of  brine,  entrance  .    .    . 
Final  temperature  of  brine,  exit  
Condenser  : 
Mean  temperature  of  cooling-water,  entrance 
Mean    temperature    of    cooling-water   from 
condenser     
Mean   temperature    of   cooling-water   from 
jacket    . 

Initial    temperature    of    condensing-  water, 
entrance    .    .    . 

Initial  temperature  of  condensing-water,  exit 
Final     temperature     of     condensing-water, 
entrance    
Final  temperature  of  condensing-water,  exit 
Error  in  heat  account,  per  cent   
Refrigerative  effect,  calories  per  horse-power 
per  hour   

Linde  machine. 

Steam-engine: 
Revolutions  per  minute      .    . 

44-9 
18.14 

IS-S3 
0.856 

9-52 
3-89 
6.00 

2     89 

0.850 

5  98 
2.89 
5-97 
2-94 

9.56 
19.76 
9-56 
19.74 
9-57 
19.74 
—1.8 

4308 

45-i 
18.26 

15.20 
0-833 

9.24 
2-95 

2.  O2 
5-02 
0.846 
2.05 

—  5-02 
2.04 
5-04 

9-54 
19.63 
9-55 
19.42 
9-54 
19-45 
—1.8 

3182 

45-1 
17-03 

14.31 
0.840 

9.00 
2-13 

—  9-99 
—  12.91 
0.843 
—  9-95 
—  12.94 
9-97 
12.89 

9.61 

19.84 
9.61 
19.82 
9.60 
19.89 
—  1.9 

2336 

44-8 
15-70 

12.63 
0.805 

8.89 
1.56 

—  17.92 
—  20.82 
0.840 
—17.97 
—  20.83 
17.96 
20.83 

9.61 
19.72 
9.64 
19.79 
9-56 
19.88 

2.1 
I7II 

45-0 
24.41 

21.86 
0.895 

14.03 
2-95 

—  2.03 
—  S-oi 
0.845 
—  2.03 
—  S-oo 
2.03 
5-oi 

9.68 
35-33 
9.68 
35-45 
9-65 
35-44 
+  i 

2022 

Horse-power 

Compressor  : 
Horse  -power    .    . 

Mechanical  efficiency  

Pressure  in  condenser,  kilograms  per  square 
centimetre     
Pressure  in  vaporizer,  kilograms  per  square 
centimetre     

Vaporizer  : 
Mean  temperature  of  brine,  entrance     .    . 
Mean  temperature  of  brine,  exit      .... 
Specific  heat  per  litre     .    .    . 

Initial  temperature  of  brine,  entrance    .    . 
Initial  temperature  of  brine,  exit  
Final  temperature  of  brine,  entrance  .    .    . 
Final  temperature  of  brine,  exit  

Condenser  : 
Mean  temperature  of  cooling-water,  entrance 
Mean  temperature  of  cooling-  water,  exit.    . 
Initial  temperature  of  water,  entrance    .    . 
Initial  temperature  of  water,  exit     .... 
Final  temperature  of  water,  entrance      .    . 
Final  temperature  of  water,  exit  

Error  in  heat  account,  per  cent   
Refrigerative  effect,  calories  per  horse-power 
per  hour   

41 8  REFRIGERATING-MACHINES 

to  be  6°C.,  --  2°  C.,  —  10°  C.,  and  —  18°  C.  The  cooling 
water  was  supplied  to  the  condenser  at  about  9°.5  C.,  for  all 
tests,  and  for  all  but  one  it  left  the  condenser  with  a  temperature 
of  nearly  20°  C.;  the  fifth  test  on  each  machine  was  made  with 
the  exit  temperature  of  the  cooling  water  at  about  35°  C. 

The  pressure  in  the  compressor  depended,  of  course,  on  the 
temperatures  of  the  brine  and  the  cooling-water.  For  all  the 
tests  except  the  fifth  on  each  machine,  the  maximum  pressure 
of  the  working  substance  was  nearly  constant :  about  9  kilograms 
per  square  centimetre  for  ammonia  and  about  4  kilograms  for 
Pictet's  fluid.  The  fifth  test  had  considerably  higher  pressure, 
corresponding  to  the  higher  temperature  in  the  condenser.  The 
minimum  pressure  of  the  working  substance  of  course  diminished 
as  the  brine  temperature  fell. 

The  heat  yielded  per  hour  to  the  ammonia  in  the  vaporizer 
was  calculated  by  multiplying  together  the  amount  of  brine  used 
in  an  hour,  the  specific  heat  of  the  brine,  and  its  increase  of 
temperature.  But  the  initial  and  final  temperatures  were  not 
quite  constant,  and  so  a  correction  was  applied.  The  heat 
abstracted  from  the  ammonia  in  the  condenser  was  calculated 
from  the  water  used  per  hour  and  its  increase  of  temperature. 
The  calculation  for  Pictet's  machine  involves  also  the  jacket- 
water  and  its  increase  of  temperature.  A  correction  is  applied 
for  the  variations  of  initial  and  final  temperatures  of  the 
cooling-water.  If  the  heat  equivalent  of  the  work  of  the  com- 
pressor is  added  to  the  heat  yielded  by  the  vaporizer  the  sum 
should  be  equal  to  the  heat  abstracted  by  the  cooling-water. 
The  per  cent  of  difference  between  these  two  calculations  of 
the  heat  abstracted  by  the  cooling-water  is  a  measure  of  the 
accuracy  of  the  tests. 

The  refrigerative  effect  is  obtained  by  dividing  the  heat  yielded 
by  the  vaporizer  by  the  horse-power  of  the  steam-cylinder.  The 
first  four  tests  with  constant  temperature  in  the  condenser  show 
a  regular  decrease  in  the  refrigerative  effect  for  each  machine 
as  the  temperature  of  the  brine  and  the  minimum  pressure  of 
the  working  substance  is  reduced.  The  fifth  test,  with  a 


TESTS    OF    COMPRESSION-MACHINES 


419 


higher  temperature  in  the  condenser,  shows  a  less  refrigerative 
effect  than  the  second  test,  which  has  nearly  the  same  brine 
temperatures.  These  results  are  in  concordance  with  the  idea 
that  a  refrigerating- machine  is  a  reversed  heat-engine;  for  a 
heat-engine  will  have  a  higher  efficiency  and  will  use  less  heat 
per  horse-power  when  the  range  of  temperatures  is  increased, 
and  per  contra,  a  refrigerating-machine  will  be  able  to  transfer 
less  heat  per  horse-power  as  the  range  of  temperatures  is 
increased. 

TABLE    XXXIX. 

TESTS  ON  AMMONIA   REFRIGERATING-MACHINE. 

By  Professor  J.  E.  DENTON,   Trans.  Am.    Soc.    Mech.  Engr.,  vol.    xii,  p.  326. 


I 

II 

III 

IV 

Pressure  above  atmosphere,  pounds  per  square  inch  : 
Ammonia  from  compressor. 

161 

Ammonia  back-pressure  

28 

8.2 

13 

27  .5 

Barometer,  inches  of  mercury. 

29  87 

Temperature,  degrees  Fahrenheit  : 
Brine,  inlet  
outlet 

36.76 

28  86 

6.27 

14.29 

28  45 

Condensing-water  inlet     

56  65 

outlet 

83  66 

8<C    4 

8s   46 

82   86 

Jacket-water,  inlet      

44  65 

°J  '4 
16   7 

46  9 

54  .3 

Ammonia-vapor  leaving  brine-tank 

29.2 

entering  compressor  

25 

10.  13 

34 

leaving  compressor                     

263 

calculated  
entering  condenser  

229 

304 

218 

260 

237 
168 

Brine,  pounds  per  minute 

2281 

942  8 

Specific  gravity  

Specific  heat         .          .                  .               

o  82 

o  78 

o  78 

o  78 

Ammonia,  Ibs.  per  min.  by  metre  

14  68 

16.67 

28.32 

from  compressor  displacement 

Heat  account,  B.T.IT,  per  minute  : 
Given  to  ammonia  bv  brine  

71876 

8824 

compressor 

27860 

25l8 

atmosphere 

l67 

3° 

Total  received  by  ammonia.  .  .                        

1  7708 

Taken  from  ammonia  by  condenser 

jackets  

608 

6*6 

atmosphere  . 

182 

•2^8 

Total  taken  from  ammonia  

18032 

10816 

18017 

Error,  per  cent  

Power,  etc.  : 
Revolutions  per  minute  

58   09 

57    7 

57  88 

";8  89 

Horse-power  steam-cylinder.                    .        

gc    o 

7*    6 

88  6 

compressor 

5r    7 

Mechanical    efficiency  

o  81 

o  8^ 

o  86 

o  83 

Refrigerative  effect: 
Tons  of  ice  (melted)  in  24  hours  

74  8 

B.T.U.  abstracted  from  brine  per  horse-power  minute     . 
Pounds  of  ice  (melted)  per  pound  of  coal. 

174 

107 

197 

196 

Table  XXXIX  gives  the  data  and  results  of  tests  made  by 
Professor  Denton  on  an  ammonia  refrigerating-machine.     The 


420  REFRIGERATING-MACHINES 

only  items  requiring  explanation  are  the  refrigerative  effect 
and  the  calculated  temperature  of  the  vapor  leaving  the  con- 
denser; the  latter  was  calculated  by  the  equation 

r,  - 

and  shows  both  the  cooling  effect  of  the  jacket  and  the  error  in 
assuming  an  adiabatic  compression.  The  exponent  used  here 
is  a  trifle  smaller  than  that  of  equation  (249)  page  407.  The 
refrigerative  effect  was  obtained  by  dividing  the  B.T.U.  given 
to  the  ammonia  in  a  minute  by  the  horse-power  of  the  steam- 
cylinder.  The  tons  per  horse-power  in  24  hours  was  obtained 
by  multiplying  the  refrigerative  effect  in  thermal  units  per 
minute  by  the  number  of  minutes  in  a  day  and  then  dividing 
the  product  by  2000  (the  pounds  in  a  short  ton)  and  by  144 
(the  heat  of  melting  a  pound  of  ice).  The  pounds  of  ice  per 
pound  of  coal  was  based  on  an  assumed  consumption  of  three 
pounds  of  coal  per  horse-power  per  hour,  and  was  calculated 
by  multiplying  the  B.T.U.  per  horse-power  per  minute  by  60 
and  dividing  by  3  X  144. 

The  main  dimensions  of  the  machine  were: 

Diameter  of  ammonia  cylinder  (single-acting)      12  inches 

Stroke  of  ammonia  cylinder 30        " 

Diameter  of  steam-cylinder      .    .    .    ,        18       " 

Stroke  of  steam-cylinder 36       " 

Diameter  of  pipe  for  vaporizer  and  condenser i       " 

Length  of  pipe  in  vaporizer 8000  feet 

condenser 5000     " 

Test  of  an  Absorption-machine.  —  The  principal  data  and 
the  results  of  a  test  made  by  Professor  J.  E.  Denton  *  on  an 
absorption  ammonia  refrigerating- machine  are  given  in  Table 
XL.  The  machine  is  applied  to  chill  a  room  of  about  400,000 
cubic  feet  capacity  at  a  pork-packing  establishment  at  New 
Haven,  Conn.  In  connection  with  this  test  the  specific  heat  of 
the  brine,  which  served  as  a  carrier  of  heat  from  the  cold  room 
to  the  ammonia,  was  determined  by  direct  experiment.  The 

*  Trans.  Am.  Soc.  Mech.  Eng.,  vol.  x,  May,  1889. 


TEST   OF  AN  ABSORPTION-MACHINE 

TABLE  XL. 

TEST  OF  AN  ABSORPTION-MACHINE. 
SEVEN  DAYS'  CONTINUOUS  TEST,  SEPT.  11-18,  1888. 


421 


Average       pressures 
above  atmosphere" 
in  Ibs.  per  sq.  in. 

I50-77 
47.70 
23.69 
23-4 
80 
272 

21.2 

16.16 

54* 
80 
80 
in 

212 
I78 
132 
272 

260 

31 

1.633.7 
II9,26o 
0.800 
40.67 

1,986 

4-1 
481,260 

243 
9l8,OOO 
I,Il6,000 

1,203 
271 

932 
36,000 

I7.I 

135 

870 

2OO 

Cooler 

^Absorber  

Average       tempera- 
tures   in    Fahren- 
heit degrees. 

Atmosphere  in  vicinity  of  machine  .... 

(Inlet 

Brinej  Outlet                           

(Inlet             

Condenser  jQirtlet                          

(  Inlet 

Absorber   j^      

(  Upper  outlet  to  generator  .... 
Heater«  Lower    "        "  absorber     .... 

Inlet  from  generator 

Water  returned  to  main  boilers  from  steam 
coil     

Average     range      of 
temperatures' 
Fahr.  degrees. 

-Brine     

Brine  circulated  per 
hour. 

Cubic  feet                         

Pounds                                                  .... 

Specific  heat  of  brine 
Cooling  capacity  of  rr 
Steam  consumption 
operate  ammonia  p 

tachine  in  tons  of  ice  per  day  of  24  hours    . 
per  hour,    to    volatilize   ammonia,   and  to 
ump  pounds      

British     thermal 
units: 

j  (  Per  Dound  of  brine 

Eliminated  J  1 
(  Total  per  hour  

Of  refrigerating  effect  per  pound  of  steam 
consumption         

Rejected{AtCOndenSer'per<fh°Ur     '   '   '    ' 

f  On  entering  generator 
coil 

Per  pound  of  steam-<  .-     , 
On  leaving  generator 

[     coil        

Consumed  by  generator  per  Ib.  of    steam 
condensed'.    ...                

Condensing  water  pel 
Equivalent  ice  produ 
evaporates  ten  pou 
Calories,  refrigerating 
Approximate     coil 
surface  in  sq.  ft. 

*  hour,  in  pounds                       

:tion  per  pound  of  coal,  if  one  pound  of  coa 
nds  of  steam  at  boiler                                   . 

;  effect  per  kilogram  of  steam  consumed    .    . 
(  Condensing  coil 

5  Absorber        "    

i  Steam              "    . 

422 


REFRIGERATING-MACHINES 


brine  chilled  and  the  cooling  water  used  were  measured  with 
meters,  which  were  afterwards  tested  under  the  conditions  of 
the  experiment. 

It  is  interesting  to  compare  the  refrigerative  effects  expressed  in 
pounds  of  ice  per  pound  of  coal.  On  this  basis  the  compression- 
machine  tested  by  Professor  Denton  has  an  advantage  of 

24.1  —17.1 

— * —  X  100  =  IQ  per  cent. 

24.1 

But  this  comparison  is  really  unfair  to  the  compression- 
machine,  for  its  steam-engine  is  assumed  to  require  a  consump- 
tion of  three  pounds  of  coal  per  horse-power  per  hour,  while  the 
calculation  for  the  absorption-machine  is  based  on  the  assumption 
that  a  pound  of  coal  can  evaporate  ten  pounds  of  water;  but  an 
automatic  condensing-engine  of  the  given  power  should  be  able 
to  run  on  20  or  22  pounds  of  steam  per  horse-power  per  hour. 


CHAPTER  XVII. 

FLOW  OF   FLUIDS. 

THUS  far  the  working  substance  has  been  assumed  to  be  at 
rest  or  else  its  velocity  has  been  considered  to  be  so  small  that 
its  kinetic  energy  has  been  neglected;  now  we  are  to  consider 
thermodynamic  operations  involving  high  velocities,  so  that  the 
kinetic  energy  becomes  one  of  the  important  elements  of  the 
problem.  These  operations  are  clearly  irreversible  and  conse- 
quently the  first  law  of  thermodynamics  only  is  available,  and  if 
any  element  of  computation  involves  reference  to  equations  that 
were  deduced  by  aid  of  the  second  law,  care  must  be  taken 
that  such  computations  are  allowable.  It  is  true  that  all  prac- 
tical thermal  operations  are  irreversible  for  one  reason  or  another; 
for  example,  the  cycle  for  a  steam  engine  is  irreversible,  both 
because  steam  is  supplied  and  exhausted  from  the  cylinder  and 
because  the  cylinder  is  made  of  conducting  material.  But  all 
adiabatic  operations  in  cylinders  (which  serve  as  the  basis  of 
theoretical  discussions)  are  properly  treated  as  reversible  and  all 
the  deductions  from  the  second  law  may  be  applied  to  that  part 
of  the  cycle.  In  particular  the  limitations  of  the  discussion  of 
entropy  on  page  32  have  been  observed. 

Three  cases  of  continuous  thermal  operations  have  been 
discussed  (i)  flow  through  a  porous  plug,  (2)  the  throttling 
calorimeter,  (3)  friction  of  air  in  pipes;  to  which  it  may  be  well 
to  return  now.  In  all,  the  velocity  of  the  fluid  has  been  so  small 
that  its  kinetic  energy  was  neglected;  in  none  of  them  was  any 
reference  made  to  equations  deduced  by  the  aid  of  the  second 
law  of  thermodynamics.  Rather  curiously,  all  the  operations 
were  adiabatic,  using  the  word  to  mean  that  no  heat  was  taken 
from  or  lost  to  external  objects ;  in  the  case  of  transmission  of  air 
in  pipes,  this  comes  from  the  natural  conditions  of  the  case 

423 


424  FLOW    OF   FLUIDS 

and  in  the  other  two  operations  there  was  careful  insulation 
from  heat.  None  of  the  operations  are  isoentropic;  for  instance, 
the  entropy  of  steam  supplied  to  the  calorimeter  on  page  192 
is  about  i. 60  and  the  entropy  of  the  superheated  steam  in  the 
calorimeter  is  about  1.72;  but  this  does  not  enter  into  the  solution 
of  the  problem  and  is  more  curious  than  useful. 

The  flow  of  fluids  through  orifices  and  nozzles  has  .become 
even  of  more  importance  than  formerly  on  account  of  the  develop- 
ment of  steam  turbines.  Thus  far  all  computations  have  been 
based  on  adiabatic  action,  and  when  attempt  is  made  to  allow 
for  friction  it  is  done  by  the  application  of  an  experimental 
factor  to  results  from  adiabatic  computations. 

The  following  is  the  customary  method  of  establishing  the 
fundamental  equation.  Suppose  that  a  fluid  is  flowing  from 

the  larger  pipe  A  into  the  pipe  E\ 
«  there  will  clearly  be  an  increase  in 

v£ (I!—.      velocity,  with  a  reduction  in  pressure. 

IP,        "  1 1  -P>  J 


|  The    first    law    of    thermodynamics 


FIG.  90  as  expressed  by  equation  (16),  page  14, 

needs  the  addition  of  a  term  to  take 

account  of  the  change  in  kinetic  energy,  and  may  be  written 

dQ  =  A  (dE  +  dW  +  dK)-t 

the  last  term  in  the  parenthesis  represents  the  increase  of  kinetic 
energy. 

Let  it  be  supposed  that  there  is  a  frictionless  piston  in  each 
cylinder;  the  piston  in  A  exerts  the  pressure  pl  on  the  fluid  in 
front  of  it,  and  the  piston  in  B  has  on  it  the  fluid  pressure  p2. 
Each  unit  of  weight  of  fluid  passing  from  A  through  the  orifice 
has  the  work  plvl  done  on  it,  while  each  pound  entering  the 
cylinder  B  does  the  work  pyv2.  The  assumption  of  pistons  is 
merely  a  matter  of  convenience,  and  if  they  are  suppressed  the 
same  conditions  with  regard  to  external  work  will  hold. 

If  the  velocity  in  A  is   Vl  the  kinetic  energy  of  one  unit  of 

V2  y  2 

weight  in  that  cylinder  is   — *-  ;  the  kinetic  energy  in  B  is  — 2- 

2£  2£ 

for  a  velocity  Vv 


FLOW    OF   FLUIDS  425 

The  intrinsic  energies  in  A  and  B  are  El  and  E2.  If  there 
is  no  heat  communicated  to  or  from  the  fluid  the  sum  of  the 
intrinsic  energy,  external  work,  and  kinetic  energy  must  remain 
constant,  so  that 

£,  +  #,»,  +  -^  =  E,  +  Ptvt  +  -*£•  ;  .    .    (255) 

this  is  the  fundamental  equation  for  the  flow  of  a  fluid. 

If  the  walls  of  the  pipes  are  well  insulated  there  will  not  be 
much  radiation  or  other  external  loss  even  if  the  pipes  have 
considerable  length,  and  in  cases  that  arise  in  practice  that  loss 
may  properly  be  neglected.  There  is  likely  to  be  a  considerable 
frictional  action  even  if  the  pipes  are  short,  and  the  logical  method 
appears  to  call  for  the  introduction  of  frictional  terms  at  this 
place.  Such  is  not  the  custom,  and  a  substitute  will  be  dis- 
cussed later. 

Usually  the  velocity  in  the  large  cylinder  A  is  small  and  the 
term  depending  on  it  may  be  neglected.  Solving  for  the  term 
depending  on  the  velocity  in  B  and  dropping  the  subscript, 
we  have 

^  =  El  -  E2  +  plVl  -  p2v2   ....     (256) 

Incompressible  Fluids.  —  There  is  little  if  any  change  of 
volume  or  of  intrinsic  energy  in  a  liquid  in  passing  through  an 
orifice  under  pressure,  so  that  the  equation  of  flow  becomes  in 
this  case 


(257) 


If  the  difference  of  pressure  is  due  to  a  difference  of  level  or 
head,  h,  we  have 

Pt-Pt**  hd, 

where  d  is  the  density,  or  weight  of  a  unit  of  volume,  and  is  the 
reciprocal  of  the  specific  volume;  consequently  equation  (257) 
reduces  to 

V2        , 
—  =  h, 


426  FLOW    OF   FLUIDS 

which  is  the  usual  equation  for  the  flow  of  a  liquid  through  a 
small  orifice. 

Flow  of  Gases.  —  The  intrinsic  energy  of  a  unit  of  weight  of 
a  gas  is 

E-  -£L 

~*-l' 

which  depends  only  on  the  condition  of  the  gas  and  not  on  any 
changes  that  have  taken  or  may  take  place.  The  equation  for 
the  flow  of  a  gas  therefore  becomes 


P      p 

2g 


At  this  place  it  is  customary  to  use  the  equation 

P2v2*  =  plVl*  ..........  (259) 

for  the  reduction  of  the  equation  (258)  just  as  though  we  were 
dealing  with  an  adiabatic  expansion  in  a  non-conducting  closed 
cylinder.  Now  the  fact  that  the  isoenergic  line  and  the  iso- 
thermal line  are  practically  identical  (page  63)  shows  that  a 
perfect  gas  has  no  disgregation  energy  and  consequently  for  an 
adiabatic  change  all  the  change  in  intrinsic  energy  is  available 
for  doing  outside  work,  which  in  this  case  is  applied  to  increasing 
the  kinetic  energy  of  the  gas,  instead  of  being  applied  to  the 
piston  of  a  compressed  air  motor.  If  this  analogy  is  allowed 
equation  (259)  may  be  used,  and  will  yield 


•     .     •    (260) 
so  that  equation  (258)  may  be  reduced  to 

••••«•> 


FLOW   OF   GASES  427 

This  equation  may  also  be  deduced  for  the 
work  of  air  in  the  cylinder  of  a  compressed 
air  motor  (Fig.  91).  The  work  of  admission 
is  pjVt',  the  work  of  expansion  is  by  equation 


F'G-  9*.  (81),  page  65. 


and  the  work  of  exhaust  is 


so  that  the  effective  work  is 


which  is  readily  reduced  to  equation  (261). 

For  the  calculation  of  velocities  it  is  convenient  to  replace  the 
coefficient  Pjvt  in  equation  (261)  by  RTV  since  pressures  and 
temperatures  are  readily  determined  and  are  usually  given,  thus 

.   (262) 

2g  '  /C   -    I  ' 

If  the  area  of  the  orifice  is  a,  then  the  volume  discharged  per 

second  is 

aV, 

and  the  weight  discharged  per  second  is 

aV 

w  = —  , 

when  v2  is  the  specific  volume  at  the  lower  pressure  and  is  equal 
to 


428  FLOW    OF   FLUIDS 

Substituting    V  from  equation    (262)   and   v2  from    (263)   and 
reducing 


The  equations  deduced  for  the  flow  of  air  apply  to  the  flow 
from  a  large  cylinder  or  reservoir  into  a  small  straight  tube 
through  a  rounded  orifice.  The  lower  pressure  is  the  pressure 
in  the  small  tube  and  differs  materially  from  the  pressure  of  the 
space  into  which  the  tube  may  deliver.  In  order  that  the  flow 
shall  not  be  much  affected  by  friction  against  the  sides  of  the 
tube  it  should  be  short  —  not  more  than  once  or  twice  its  diameter. 
The  flow  does  not  appear  to  be  affected  by  making  the  tube 
very  short,  and  the  degree  of  rounding  is  not  important;  the 
equations  for  the  flow  of  both  air  and  steam  may  be  applied 
with  a  fair  degree  of  approximation  to  orifices  in  thin  plates  and 
to  irregular  orifices. 

Professor  Fliegner  *  made  a  large  number  of  experiments  on  the 
flow  of  air  from  a  reservoir  into  the  atmosphere,  with  pressures 
in  the  reservoir  varying  from  808  mm.  of  mercury  to  3366  mm. 
He  used  two  different  orifices,  one  4.085  and  the  other  7.314  mm. 
in  diameter,  both  well  rounded  at  the  entrance. 

He  found  that  the  pressure  in  the  orifice,  taken  by  means  of 
a  small  side  orifice,  was  0.5767  of  the  absolute  pressure  in  the 
reservoir  so  long  as  that  pressure  was  more  than  twice  the  atmos- 
pheric pressure;  under  such  conditions  the  pressure  in  the  orifice 
is  independent  of  the  pressure  of  the  atmosphere. 

If  the  ratio  —  2  is  replaced  by  the  number  0.5767  and  if  K  is 

Pi 

replaced  by  its  value  1.405  in  equation  (264)  we  shall  have  for 
the  equation  foi  the  flow  of  a  gas 


W  =  0.482  2«y-  .....     (265) 

*  Der  Civilingenicur,  vol.  xx,  p.  14,  1874. 


FLIEGNER'S    EQUATIONS    FOR   FLOW    OF  AIR  429 

For  the  flow  into  the  atmosphere  from  a  reservoir  having  a 
pressure  less  than  twice  the  atmospheric  pressure  Fliegner  found 
the  empirical  equation 


a,  =  0.9644* 

where  pa  is  the  pressure  of  the  atmosphere. 

These  equations  were  found  to  be  justified  by  a  comparison 
with  experiments  on  the  flow  of  air,  made  by  Fliegner  himself, 
by  Zeuner,  and  by  Weisbach. 

Although  these  equations  were  deduced  from  experiments 
made  on  the  flow  of  air  into  the  atmosphere,  it  is  probable  that 
they  may  be  used  for  the  flow  of  air  from  one  reservoir  into 
another  reservoir  having  a  pressure  differing  from  the  pressure 
of  the  atmosphere. 

Fliegner' s  Equations  for  Flow  of  Air.  —  Introducing  the 
values  for  g  and  R  in  the  equations  deduced  by  Fliegner,  we  have 
the  following  equations  for  the  French  and  English  systems  of 
units : 

French  units. 


Pl 

>    2pa, 

w  =  0.3950  -^; 

Pi 

<    2pa, 

t/Pa    (Pl    ~  Pa) 

av      TI 

English  units. 

Pl 

>    2pa, 

w  =  0.5300     *-!_•  ; 

VT1 
i 

b    . 

f   o<h 

Pi   =  pressure  in  reservoir; 
pa   =  pressure  of  atmosphere; 

Tj  =  absolute  temperature  of  air  in  reservoir   (degrees  centi- 
grade, French  units;  degrees  Fahrenheit,  English  units). 


43° 


FLOW    OF    FLUIDS 


In  the  English  system  pl  and  pa  are  pounds  per  square  inch, 
and  a  is  the  area  of  the  orifice  in  square  inches,  while  w  is  the 
flow  of  air  through  the  orifice  in  pounds  per  second.  If  desired, 
the  area  may  be  given  in  square  feet  and  the  pressures  in  pounds 
on  the  square  foot,  as  is  the  common  convention  in  thermo- 
dynamics. 

In  the  French  system  w  is  the  flow  in  kilograms  per  second. 
The  pressures  may  be  given  in  kilograms  per  square  metre 
and  the  area  a  in  square  metres;  or  the  area  may  be  given  in 
square  centimetres,  and  the  pressures  in  kilograms  on  the  same 
unit  of  area.  If  the  pressures  are  in  millimetres  of  mercury, 
multiply  by  13.5959;  if  in  atmospheres,  multiply  by  10333. 

Theoretical  Maxima.  —  From  a  discussion  of  the  mean  velocity 
of  molecules  of  a  gas  Fliegner  deduces  for  the  maximum  velocity 
through  an  orifice 


V  max  =      gRTt  =  16.9 

in  metric  units.     His  ratio  of  pressure  0.5767  inserted  in  equation 
(262)  gives 

V  max  =  17.1    Vl\. 

The  algebraic  maximum  of  equation  (264)  occurs  for  the 
ratio  p2  -f-  p1  =  0.5274,  but  this  figure  probably  has  no  physical 
significance. 

Flow  of  Saturated  Vapor.  —  For  a  mixture  of  a  liquid  and  its 
vapor  equation  (no),  page  95,  gives 


so  that  equation  (256)  gives  for  the  adiabatic  flow  from  a  recep 
tacle  in  which  the  initial  velocity  is  zero 

V2       i 

—  =^  (?!  -  ^2  +  *iPi 

Substituting  for  vl  and  v2  from 

v  =  xu  +  <r, 


FLOW   OF   SATURATED   VAPOR  43l 


But 

p  +  Apu  =  r\ 

V2 
.'.     A  —  =  xlrl  -  */2  +  q,  -  q2  +  Ac-  (pl  -  pj. 

The  last  term  of  the  right-hand  member  is  small,  and  fre- 
quently can  be  omitted,  in  which  case  the  right-hand  member  is 
the  same  as  the  expression  for  the  work  done  per  pound  of  steam 
in  a  non-conducting  engine,  equation  (143),  page  136,  except 
that  as  in  that  place  the  steam  is  assumed  to  be  initially  dry,  xl 
is  then  unity.  The  intrinsic  energy  depends  only  on  the  con- 
dition of  the  steam,  and  consequently  reference  to  the  second 
law  of  thermodynamics  first  comes  into  this  discussion  with 
the  proposal  to  compute  the  quality  x2  in  the  orifice  by  aid  of 
the  standard  equation  for  entropy 


T  l  T1 

1   1  •*  2 


the  acceptance  of  this  method  infers  that  the  flow  of  steam 
through  a  nozzle  differs  from  its  action  in  the  cylinder  of  an 
engine  in  that  the  work  done  is  applied  to  increasing  the  kinetic 
energy  of  the  steam  instead  of  driving  the  piston. 

Values  of  the  right-hand  member  of  equation  (268)  may  be 
found  in  the  temperature-entropy  table  which  was  computed 
for  solving  problems  of  this  nature. 

The  weight  of  fluid  that  will  pass  through  an  orifice  having 
an  area  of  a  square  metres  or  square  feet  may  be  calculated  by 
the  formula 


+  a- 


(268) 


The  equations  deduced  are  applicable  to  all  possible  mixtures 
of  liquid  and  vapor,  including  dry  saturated  steam  and  hot 
water.  In  the  first  place  steam  will  be  condensed  in  the  tube, 
and  in  the  second  water  will  be  evaporated. 


432 


FLOW   OF   FLUIDS 


If  steam  blows  out  of  an  orifice  into  the  air,  or  into  a  large 
receptacle,  and  comes  to  rest,  the  energy  of  motion  will  be  turned 
into  heat  and  will  superheat  the  steam.  Steam  blowing  into  the 
air  will  be  wet  near  the  orifice,  superheated  at  a  little  distance, 
and  if  the  air  is  cool  will  show  as  a  cloud  of  mist  further  from  the 
orifice. 

Rankine's  Equations.  —  After  an  investigation  of  the  experi- 
ments made  by  Mr.  R.  D.  Napier  on  the  flow  of  steam,  Rankine 
concluded  that  the  pressure  in  the  orifice  is  never  less  than  the 
pressure  which  gives  the  maximum  weight  of  discharge,  and 
that  the  discharge  in  pounds  per  second  may  be  calculated  by 
the  following  empirical  equations: 

PI  =  °r  >  |  A«  w  =  a^; 

Pl  <  ^Pa,  W   =    0.029  a  [Pa   (Pi   ~   #a)]*> 

o 

in  which  p^  is  the  pressure  in  the  reservoir,  pa  is  the  pressure  of 
the  atmosphere,  both  in  pounds  on  the  square  inch,  and  a  is  the 
area  in  square  inches. 

The  error  of  these  equations  is  liable  to  be  about  two  per  cent ; 
but  the  flow  through  a  given  orifice  may  be  known  more  closely 
if  tests  are  made  on  it  at  or  near  the  pressure  during  the  flow, 
and  a  special  constant  is  found  for  that  orifice. 

Grashoff's  Formula.  —  For  pressures  exceeding  five-thirds 
of  the  external  or  back  pressure  Grashoff  gives  the  following 
formula  for  the  discharge  of  steam  through  a  converging  orifice, 

w  =  15.26  apQ-97 

the  weight  being  in  grams  per  second,  the  area  in  square  centi- 
metres and  the  pressure  in  kilograms  per  square  centimetre. 
For  English  units  the  equation  becomes 

w  =  0.0165  ap*-91 

the  discharge  being  in  pounds  per  second,  the  area  in  square 
inches  and  the  pressure  in  pounds  absolute  per  square  inch. 
Rateau  shows  that  this  formula  is  well  verified  by  his  experiments 


FLOW    OF   SUPERHEATED   STEAM 


433 


on  the  flow  of  steam,  and  that  when  the  pressure  is  less  than 
that  required  by  the  formula  the  flow  can  be  represented  by  a 
curve  which  has  for  coordinates  the  ratio  of  the  back  pressure 
to  the  internal  pressure  and  the  ratio  of  the  actual  discharge  to 
that  computed  by  the  equation  on  the  preceding  page. 
The  following  values  were  taken  from  his  curves: 


Ratio  of  back  pressure 
to  internal  pressure. 

Ratio  of  actual  to  computed  discharge. 

Converging  orifice. 

Orifice  in  thin  plates. 

o-9S 

0-45 

0.30 

0.90 

0.62 

0.42 

0.85 

o-73 

0.51 

0.80 

0.82 

0.58 

o-75 

0.89 

0.64 

0.70 

0.94 

0.69 

0.65 

0.97 

°-73 

0.60 

0.99 

0.77 

°-55 

0.80 

0.45 

0.82 

0.40 

0.83 

He  further  gives  a  curve  for  the  discharge  from  a  sharp-edged 
orifice  from  which  the  third  column  was  taken. 

Flow  of  Superheated  Steam.  —  Though  there  is  no  convenient 
expression  for  the  intrinsic  energy  of  superheated  steam,  and 
though  the  general  equation  (256)  cannot  be  used  directly,  an 
equation  for  velocity  can  be  obtained  by  the  addition  of  a  term 
to  equation  (268)  to  allow  for  the  heat  required  to  superheat 
one  pound  of  steam,  making  it  read 


F2         C* 

—=  Jti 


cdt 


The  accompanying  equation  for  finding  the  quality  of  steam  x2  is 


•  •  •<"»> 


Here  /  and  T  are  the  thermometric  and  the  absolute  temper- 
atures of  the  superheated  steam,  tl  is  the  temperature  of  saturated 
steam  at  the  initial  pressure,  and  t2  the  temperature  at  the  final 


434  FLOW    OF    FLUIDS 

pressure,  and  the  letters  r1  and  r2  and  0X  and  #2  represent  the 
corresponding  heats  of  vaporization  and  entropies  of  the  liquid. 

Both  equations  apply  only  if  the  steam  becomes  moist  at  the 
lower  pressure,  which  is  the  usual  case.  They  may  obviously 
be  modified  to  apply  to  steam  that  remains  superheated,  but 
such  a  form  does  not  appear  to  have  practical  application. 

The  method  of  reduction  of  the  integrals  in  equation  (269) 
and  (270)  is  given  on  page  114;  attention  is  called  to  the  fact 
that  the  temperature-entropy  table  affords  ready  solution  of 
equation  (269),  also  of  the  velocity  flow  during  which  the  steam, 
remains  superheated. 

Flow  in  Tubes  and  Nozzles.  —  The  velocity  of  air  or  steam 
flowing  through  a  tube  or  nozzle  with  a  large  difference  in  pressure 
is  very  high,  reaching  3000  feet  a  second  in  some  cases;  and 
consequently  the  effect  of  friction  is  marked  even  in  short  tubes 
and  nozzles.  A  test  by  Biichner  *  on  a  straight  tube  3.52  inches 
long  and  0.158  of  an  inch  internal  diameter,  under  an  absolute 
pressure  of  177  pounds  to  the  square  inch  delivered  only  about 
0.9  of  the  amount  of  steam  calculated  by  the  adiabatic  method, 
and  the  pressure  in  the  tube  fell  gradually  from  131  pounds  near 
the  entrance  to  14.5  pounds  near  the  exit  when  delivering  to  a 
condenser  at  about  atmospheric  pressure.  If  there  were  any 
use  for  such  a  device  in  engineering  the  problem  would  appear 
to  call  for  a  method  of  dealing  with  friction  resembling  that  on 
page  380  for  flow  of  air  in  long  pipes,  but  probably  more  difficulty 
would  be  found  in  getting  a  satisfactory  treatment. 

From  the  investigations  that  have  been  made  on  the  flow  of 
steam  through  nozzles  it  appears  that  they  should  have  a  well- 
rounded  entrance,  the  radius  of  the  curve  of  the  section  at  entrance 
being  half  to  three-fourths  of  the  diameter  of  the  smallest 
section  or  throat;  from  the  throat  the  nozzles  should  expand 
gradually  to  the  exit,  avoiding  any  rapid  change  of  velocity, 
as  such  a  change  is  likely  to  roughen  the  surface  where  it  occurs. 
The  longitudinal  section  may  well  be  a  straight  line  joined  to 
the  entrance  section  by  a  curve  of  long  radius.  The  taper  of 

*  Meitteilungen  iiber  Forschungrarbeiten  Heft,  18,  p.  43. 


FRICTION    HEAD 


435 


the  cone  may  be  one  in  ten  or  twelve;  this  will  give  for  the  total 
angle  at  the  apex  of  the  cone  5°  to  6° ;  if  the  entrance  to  the  nozzle 
is  not  well  rounded  there  will  be  a  notable  acceleration  of  the 
steam  approaching  the  nozzle  and  this  acceleration  outside  of 
the  nozzle  appears  to  diminish  the  amount  of  steam  that  the 
nozzle  can  deliver.  The  expansion  should  preferably  be  suffi- 
cient to  reduce  the  steam  to  the  pressure  into  which  the  nozzle 
delivers;  otherwise  the  acceleration  of  the  steam  will  continue 
beyond  the  nozzle,  but  the  steam  tends  more  and  more  to  mingle 
with  the  adjacent  fluid  through  which  it  moves,  and  a  poorer 
effect  is  likely  to  be  obtained. 

If  the  expansion  in  the  nozzle  is  not  enough  to  reduce  the 
pressure  of  the  steam  to  (or  nearly  to)  the  external  pressure  into 
which  the  nozzle  delivers,  sound  waves  will  be  produced  and 
there  will  be  irregular  action,  loss  of  energy,  and  a  distressing 
noise.  On  the  other  hand  if  the  expansion  in  the  nozzle  reduces 
the  pressure  of  the  steam  below  the  external  pressure  at  the 
exit,  sound  waves  will  be  set  up  in  the  nozzle  with  added  resist- 
ance. This  latter  condition  is  likely  to  be  worse  than  the 
former,  and  if  the  pressures  between  which  the  nozzle  acts 
cannot  be  controlled  it  should  be  so  designed  as  to  expand 
the  steam  to  a  pressure  a  little  higher  than  that  against  which 
it  is  expected  to  deliver,  allowing  a  little  acceleration  to  occur 
beyond  the  nozzle. 

Friction  Head.  —  In  dealing  with  a  resistance  to  the  flow  of 
water  through  a  pipe,  such  as  is  caused  by  a  bend  or  a  valve, 
it  is  customary  to  assume  that  the  resistance  is  proportional  to 
the  square  of  the  velocity  and  to  modify  equation  (258),  page 
425  to  read 

F2  F2 

h  =  —  +  C—> 

2g  2g 

where  C  is  a  factor  to  be  obtained  experimentally.  The  term 
containing  this  factor  is  sometimes  called  the  head  due  to  the 
resistance  or  required  to  overcome  the  resistance,  and  the 
equation  may  be  changed  to 


436  FLOW   OF   FLUIDS 

V2 

h  =  v—  +  V; 

2£ 

it  being  understood  that  of  the  available  head  h,  a  certain  portion 
h'  is  used  up  in  overcoming  resistances  and  the  remainder  is 
used  in  producing  the  velocity  V.  This  aspect  is  well  expressed 
by  shifting  h'  to  the  other  side  of  the  equation  and  writing 


This  method  has  been  used  by  writers  on  steam  turbines  to 
allow  for  frictional  and  other  resistance  and  losses.  It  must 
be  admitted  that  it  is  a  rough  and  unsatisfactory  method,  but 
perhaps  it  will  serve.  The  value  of  y  probably  varies  between 
0.05  and  0.15  for  flow  through  a  single  nozzle  or  set  of  guide 
blades  or  moving  buckets  in  a  steam  turbine. 

There  is  one  difference  between  the  behavior  of  water  and 
an  elastic  fluid  like  air  or  steam  that  must  be  clearly  understood, 
and  kept  in  mind.  Frictional  resistance  and  other  resistances 
to  the  flow  of  water,  transform  energy  into  heat  and  that  heat 
is  lost,  or  if  it  is  kept  by  the  water  is  not  available  afterwards 
for  producing  velocity;  on  the  other  hand  the  energy  which 
is  expended  in  overcoming  frictional  or  other  resistances  of 
like  nature  by  steam  or  air,  is  changed  into  heat  and  remains  in 
the  fluid,  and  may  be  available  for  succeeding  operations. 

Experiments  on  Flow  of  Steam.  —  There  are  five  ways  of 
experimenting  on  the  flow  of  steam  through  orifices  and  nozzles 
that  have  been  applied  to  test  the  theory  of  flow.  Some  of  them, 
used  separately  or  in  combination,  can  be  made  to  give  values 
of  the  friction  factor  y. 

(1)  Steam  flowing  through   an    orifice  or  a   nozzle   may   be 
condensed  and  weighed. 

(2)  The  pressure  at  one  or  several  points  in  a  nozzle  may 
be  measured  by  side  orifices  or  by  a  searching-  tube  ;  the  latter 
may   be  used   to  investigate  the  pressure  in  the  region  of  the 
approach  to  the  entrance,  or  in  the  region  beyond  the  exit,  and 
may  also  be  used  with  an  orifice. 


BUCHNER'S   EXPERIMENTS  437 

(3)  The  reaction  of  steam  escaping  from  a  nozzle  01  an  orifice 
may  be  measured. 

(4)  The  jet  of  steam  may  be  allowed  to  impinge  on  a  plate 
or  curved  surface  and  the  impulse  may  be  measured. 

(5)  A  Pitot    tube    may  be    introduced  into   the  jet  and  the 
pressure  in  the  tube  can  be  measured. 

Of  course  two  or  more  of  the  methods  may  be  used  at  the  same 
time  with  the  greater  advantage.  It  will  be  noted  that  none  of 
the  methods  alone  or  in  combination  can  be  made  to  determine 
the  velocity  of  the  steam,  and  that  all  determinations  of  velocity 
equally  depend  on  inference  from  calculations  based  on  the 
experiments. 

Formerly  the  weight  of  steam  discharged  was  considered  of 
the  greatest  importance,  as  in  the  design  of  safety-valves,  or  in 
the  determination  of  the  amount  of  steam  used  by  auxiliary 
machines  during  an  engine-test.  The  first  method  of  experi- 
menting was  obviously  the  most  ready  method  of  determining 
this  matter,  and  was  first  applied  by  Napier  in  1869,  and  on  his 
results  were  based  Rankine's  equations. 

Since  the  development  of  steam  turbines  much  importance  is 
given  to  determination  of  steam  velocities,  though  it  is  probable 
that  the  determination  of  areas  is  still  the  more  important 
method,  as  on  it  depends  the  distribution  of  work  and  pressure, 
while  a  considerable  deviation  from  the  best  velocity  will  have 
an  unimportant  influence  on  turbine  efficiency.  The  first 
experiments  on  reaction  were  by  Mr.  George  Wilson  in  1872, 
but  as  his  tests  did  not  include  the  determination  of  the  weight 
discharged  they  are  less  valuable. 

Biichner's  Experiments.  —  A  number  of  experimenters  have 
determined  the  weight  of  steam  discharged  by  nozzles  and  tubes 
and  at  the  same  time  measured  the  pressure  in  side-orifices  at 
one  or  more  places.  The  most  complete  appear  to  be  those  of 
Dr.  Karl  Buchner  *  on  the  flow  through  tubes  and  nozzles. 
Omitting  the  tests  on  tubes  and  on  nozzles  with  a  very  small 

*  Mitteilungen  uber  Forschungsarbeiten  Heft  18,  p.  47. 


43^ 


FLOW    OF    FLUIDS 


taper,  the  nozzles  for  which  results  will  be  quoted  have  the  fol- 
lowing designations  and  dimensions: 


NOZZLES  TESTED   BY   DR.    BUCHNER,   ALL  DIMENSIONS   IN 

INCHES. 


Designa- 
tion. 

Total 
length. 

Cylindri- 
cal part. 

Conical 
part. 

Diameter 
at  throat. 

Taper 
one  in. 

Distance 
first  side 
orifice 
from 
entrance. 

Distance 
last  side 
orifice 
from  exit. 

2a 

1.97 

0.36 

.61 

0.158 

2O 

o-33 

0.17 

2b 

1.97 

0.36 

.61 

0.158 

13 

0.33 

0.17 

3a 

0-945 

0-37 

-365 

0-159 

7.2 

0.34 

0.14 

3b 

0-945 

o-37 

.365 

0.159 

4-9 

0.34 

o.  14 

5C 

i-37 

o-37 

.OO 

O.2OO 

20.3 

0.24 

O.II 

5d 

i-37 

o-37 

.00 

0.20O 

14.2 

0.24 

O.II 

All  the  nozzles  had  a  cylindrical  portion  for  which  the  length 
is  given  in  the  above  table  including  the  rounding  at  entrance. 
Excluding  the  rounding,  this  cylindrical  portion  was  two  or  three 
times  the  diameter  at  the  throat  and  appears  to  have  had  consid- 
erable influence  on  the  distribution  of  the  pressure.  There  were 
from  one  to  three  additional  side  orifices  evenly  distributed; 
from  pressure  in  these  orifices  Buchner  makes  interesting  com- 
putations concerning  the  behavior  of  the  fluid  in  the  tube,  but 
the  results  are  not  different  from  those  that  are  brought  out  by 
the  investigations  of  Stodola  and  are  not  included  in  this  dis- 
cussion. The  data  and  results  from  such  of  the  tests  as  appear 
to  bear  on  our  present  purpose  of  investigating  the  discharge  and 
friction  of  nozzles  are  given  on  page  439. 

Steam  for  these  tests  was  taken  from  a  boiler  through  a  sepa- 
rator which  probably  delivered  steam  with  a  fraction  of  a  per  cent 
of  priming.  The  pressures  were  all  measured  on  one  gauge  by 
aid  of  an  eight- way-cock.  The  steam  from  the  nozzles  was  con- 
densed and  weighed;  the  experimenter  estimates  the  error  due 
to  uncertainty  of  draining  the  condenser  at  two  per  cent,  which 
appears  to  be  the  maximum  error  to  be  attributed  to  any  of  the 


BUCHNER'S   EXPERIMENTS 


439 


results.  The  discharge  was  also  computed  by  GrashofPs 
equation  on  page  432,  and  the  ratio  to  the  actual  discharge  is 
that  set  down  in  the  table;  the  variation  from  unity  is  not  greater 
than  the  probable  maximum  error.  The  method  of  the  compu- 
tation of  velocities  at  throat  and  exit  by  the  experimenter  is  not 
very  clear,  but  it  was  made  to  depend  on  the  equation  (268),  using 
the  proper  pressure  and  the  discharge  computed  by  GrashofPs 
equation. 

TESTS   ON   FLOW  OF   STEAM. 
DR.  KARL  BUCHNER. 


Number 
and 
designa- 

Pressure pounds  absolute. 

Ratio  of 
throat  to 
initial. 

Dis- 
charge 
pounds 
per 

Ratio 
of  actual 
to  com- 
puted 

Velocity 
at  throat 

Velocity 
at  exit. 

Ratio 
of  actual 
to  com- 
puted 

tion. 

Initial 

Throat. 

Exit. 

External 

second. 

dis- 
charge . 

velocity. 

i-2a 

182 

104.4 

25-3 

13.6 

o-573 

0.0503 

1800 

3030 

0.928 

2-2E 

160.5 

94-4 

21.7 

13.6 

°-577 

0  .  0449 

•*          0 

"S.  o  °£ 

1790 

3020 

0.930 

3-2a 

147-3 

83.0 

20.7 

13-8 

0.564 

0.0411 

o       6 

1820 

2990 

0.926 

4-2a 

I3I-3 

75  -1 

18.5 

0.572 

0.0370 

1790 

2990 

0.929 

5-2a 

117.1 

67.6 

16.8 

13.8 

0-577 

0.0331 

1780 

2960 

0.925 

33~2b 

180.2 

92.1 

16.5 

14.1 

0.511 

o  .  0494 

1940 

3260 

0.920 

36-3* 

149.9 

76.8 

21  .2 

13-6 

0.529 

0.0394 

•*       o 

1860 

3060 

0-957 

37~3a 

I3I-5 

70.4 

19-5 

13-8 

0-535 

0.0363 

Os  i-    ON 

1850 

3020 

0.950 

38-3a 

II5-7 

62.0 

17.4 

13-8 

o.536 

0.0219 

O           O 

1850 

3020 

0-944 

39-3  b 

183.6 

99.6 

l8-5 

i8.S 

0.541 

0.0501 

... 

1830 

343° 

0.987 

4i-5b 

103.0 

68.6 

38.1 

15-4 

0.660 

o  .  0483 

155° 

2190 

0.932 

42-5b 

89.3 

58.7 

32.8 

14.9 

0.658 

0.0419 

°0           « 

J550 

2180 

0.932 

43  -5  b 

75-2 

49-3 

27.9 

14.7 

0.656 

0.0343 

*&£  o 

1560 

2150 

0.923 

44-5  b 

61  .0 

37-6 

22.3 

14-5 

0.643 

0.0282 

O           M 

1560 

2160 

0.929 

45-5  b 

45-4 

28.0 

16.9 

14-5 

0.618 

O.O2II 

1630 

2130 

0.923 

47~5C 

102.5 

65-4 

25-9 

15.0 

0.637 

0.0549 

1630 

2520 

0.927 

48-50 

88.8 

55-7 

22.2 

14.8 

°-635 

O.04IO 

*^              H 

1630 

^530 

0.931 

49-5C 

74.2 

46.9 

l8-5 

14.6 

0.633 

o  .  0344 

o  3  o 

1620 

2530 

0-935 

5°-Sc 

59-2 

37-i 

14-9 

14.4 

0.625 

0.0277 

H                ^ 

1630 

2490 

0.932 

The  nozzles  30  and  36  had  tapers  of  1 17.2  and  1 14.9  which  were 
probably  too  great,  so  that  they  may  not  have  been  filled  with 


440  FLOW    OF    FLUIDS 

steam;  this  might  account  for  the  small  ratio  of  the  throat  to  the 
initial  pressure;  the  nozzle  26,  which  had  a  taper  of  1:13,  also 
shows  a  small  ratio  of  throat  to  initial  pressure. 

The  most  interesting  feature  of  the  tests  is  the  ratio  of  the 
velocity  at  exit,  computed  by  the  method  referred  to  above,  from 
the  pressure  at  the  side  orifice  near  the  exit  from  the  nozzle.  This 
does  not  appear  to  depend  on  the  throat  pressure.  Leaving 
out  tests  on  the  nozzles  30  and  3^  the  mean  value  of  this  ratio  is 
about  0.93  which  corresponds  to  a  value  y  =  0.14. 

Rateau's  Experiments.  —  These  tests  *  have  already  been 
referred  to  in  connection  with  Grashoff's  formula.  They  differ 
from  most  tests  on  the  discharge  from  orifices  and  nozzles  in 
that  the  steam  was  condensed  by  a  stream  of  cold  water  which 
formed  a  jet  condenser;  the  amount  of  steam  was  computed 
from  the  rise  of  temperature  and  the  amount  of  cold  water  used, 
which  latter  was  determined  by  flowing  it  through  an  orifice. 
He  estimates  his  error  at  something  less  than  one  per  cent.  The 
number  of  tests  is  too  large  to  quote  here;  it  may  be  enough  to 
say  that  his  diagrams  show  a  very  great  regularity  in  his  results, 
so  that  whatever  error  there  may  be  is  to  be  attributed  to  the 
method,  which  does  avoid,  as  he  claims,  the  uncertainty  of 
draining  a  condenser. 

Kneass'  Experiments.  —  In  order  to  determine  the  pressure 
in  steam-nozzles  such  as  are  used  in  injectors,  Mr.  Strickland  L. 
Kneass  f  made  investigations  with  a  searching-tube,  having  a 
small  side  orifice,  both  when  the  nozzles  were  performing  their 
usual  function  in  an  injector  and  when  discharging  freely  into 
the  atmosphere.  He  also  used  side  orifices  bored  through  the 
nozzles  for  the  same  purpose.  The  most  interesting  feature  of 
his  investigation  is  that  it  makes  practically  no  difference  whether 
the  discharge  is  free  or  into  the  combining  tube  of  an  injector. 

*  Experimental  Researches  on  Flow  of  Steam,  trans.  H.  B.  Brydon. 
t  Practice  and  Theory  of  the  Injector.     J.  Wiley   &  Sons,  1894. 


ROSENHAIN'S    EXPERIMENTS  44! 

For  a  well-rounded  nozzle  such  as  is  used  for  an  injector  having 
a  taper  of  one  to  six,  he  found  the  following  results  : 

Absolute  Pressure.  Calculated   Veloc- 

Initial.                   Throat.  Ratio.  ity  at  Throat. 

135                         82.0  0.606  1407 

105                         61.5  0.585  1448 

75                       42  0.559  1491 

45                       24.5  0.546  1504 

Stodola's  Experiments.  —  In  his  work  on  Steam  Turbines, 
Professor  Stodola  gives  the  results  of  tests  made  by  himself  on  the 
flow  of  steam  through  a  nozzle,  having  the  following  proportions: 
diameter  at  throat  0.494,  diameter  at  exit  1.45,  and  length  from 
throat  to  exit  6.07,  all  in  inches.  The  nozzle  had  the  form  of  a 
straight  cone  with  a  small  rounding  at  the  entrance;  the  taper  was 
i  :6.37.  Four  side  orifices  and  also  a  searching-tube  were  used  to 
measure  the  pressure  at  intervals  along  the  nozzle;  the  searching- 
tube  was  a  brass  tube  0.2  of  an  inch  external  diameter  closed  at 
the  end  and  with  a  small  side  orifice.  This  orifice  was  properly 
bored  at  right  angles;  two  other  tubes  with  orifices  inclined, 
one  45°  against  the  stream  and  one  45°  down  stream,  gave  results 
that  were  too  large  and  two  small  by  about  equal  amounts. 

Stodola  made  calculations  with  three  assumptions  (i)  with  no 
frictional  action,  (2)  with  ten  per  cent  for  the  value  of  y,  and  (3) 
with  twenty  per  cent ;  comparing  curves  obtained  in  this  way  for 
the  distribution  of  pressures  with  those  formed  by  experiments, 
he  concludes  that  the  value  of  y  for  this  nozzle  was  fifteen  per  cent. 

Rosenhain's  Experiments.  —  The  most  recent  and  notable 
experiments  on  flow  of  steam  with  measurement  of  reactions 
were  made  at  Cambridge  by  Mr.  Walter  Rosenhain.*  Steam 
was  brought  from  a  boiler  through  a  vertical  piece  of  cycle- 
tubing  to  a  chamber  which  carried  the  orifices  and  nozzles  at  its 
side;  the  reaction  was  counteracted  by  a  wire  that  was  attached 
to  the  chamber  passed  over  an  antifriction  pulley  to  a  scale 
pan,  to  which  the  proper  weight  could  be  added.  Afterwards 
he  determined  the  discharge  by  collecting  and  weighing  steam 

*  Proc.  Inst.  Civ.  Eng.,  vol.  cxl,  p.  199. 


442 


FLOW    OF    FLUIDS 


under  similar  conditions.  The  steam  pressure  was  controlled  by 
a  throttle-valve.  It  is  probable  that  there  was  some  moisture  in 
the  steam  at  high  pressures  and  that  at  low  pressures  the  steam 
was  slightly  superheated.  The  following  table  gives  the  dimen- 
sions of  the  nozzles : 

ROSENHAIN'S     EXPERIMENTS    DIMENSIONS. 


Designation. 

Least  Diameter. 

Greatest  Diameter. 

Taper. 

I 

0.1873 

II 

o.  1840 

0.287 

I       20 

IIA 

0.1866 

. 

IIB 

0.1849 

0.287 

I     20 

III 

0.1882 

0.368 

I       12 

IIIA 

0.1882 

°-2S5 

I       12 

IIIB 

0.1882 

0.241 

I       12 

IV 

0.1830 

0-255 

I       30 

IVA 

0.1830 

0.242 

I       30 

IVB 

o.  1830 

0.230 

I       30 

IVC 

0.1830 

0.217 

I       30 

IVD 

o.  1830 

0.205 

I       30 

I  was  an  orifice  with    sharp  edge;    IIA  had  a  sharp  edge  at  entrances;    the 
several  orifices  numbered  III  and  IV  had  slightly  rounded  entrances. 

DATA    AND   RESULTS. 


Velocities. 

Nozzle. 

Ratio  of 
diameter. 

Proper  initial 
pressure  . 

Coefficient 
of  friction. 

Adiabatic 

Expt. 

Ratio. 

II 

1.56 

150 

2900 

2740 

0.946 

o.  105 

III 

1.96 

275 

3280 

IIIA 

1.36 

97i 

2600 

2530 

0.972 

0.045 

IIIB 

1.28 

80 

2460 

2220 

0.903 

0.185 

IV 

i-39 

i°5 

2630 

240O 

0.913 

0.166 

IVA 

1.32 

90 

2520 

2340 

0.929 

0.137 

IVB 

1.26 

77* 

2440 

22OO 

0.901 

0.188 

IVC 

1.19 

62* 

2220 

2030 

0.914 

0.165 

IVD 

1.  12 

5° 

2100 

1920 

0.914 

0.165 

A  calculation  has  been  made  by  the  adiabatic  method  to 
determine  the  pressures  for  which  the  several  nozzles  tested 
would  expand  the  steam  down  to  the  pressure  of  the  atmosphere; 


PRESSURE  IN  THE  THROAT  443 

a  direct  calculation  cannot  be  made,  but  a  curve  can  readily  be 
determined  from  which  the  pressure  can  be  interpolated.  The 
velocities  corresponding  to  these  pressures  have  been  taken  from 
Rosenhain's  curves  and  the  velocities  were  calculated  also  by  the 
adiabatic  method.  Since  the  diagrams  in  the  Proceedings  are  to 
a  small  scale  the  deduction  of  pressures  from  them  cannot  be  very 
satisfactory,  but  the  results  are  probably  not  far  wrong.  The 
table  on  page  442  gives  the  coefficient  of  friction  obtained  by 
this  method. 

Lewicki's  Experiments.  —  These  experiments  were  made  by 
allowing  the  jet  of  steam  to  impinge  on  a  plate  at  right  angles 
to  the  stream,  and  measuring  the  force  required  to  hold  the  plate 
in  place;  from  this  impulse  the  velocity  may  be  determined. 
It  was  found  necessary  to  determine  by  trial  the  distance  at 
which  the  greatest  effort  was  produced.  One  of  his  nozzles  had 
for  the  least  diameter  0.237  and  for  the  greatest  diameter  0.305 
of  an  inch  or  a  ratio  of  1.28,  which  is  proper  for  a  pressure  of  80 
pounds  per  square  inch  absolute.  His  experiments  gave  the 
following  results  as  presented  by  Biichner: 

Steam  pressure 77         99         108 

Ratio  of  computed  and  ) 

expt.  velocities  |   -    -    -     0.96  0.955 

Coefficient  of  friction      ....     0.08     0.08       0.09 

These  experiments  like  those  for  reaction  are  liable  to  be  vitiated 
by  expansion  and  acceleration  of  the  steam  beyond  the  orifice. 

Pressure  in  the  Throat.  —  Some  of  the  tests  by  Biichner  show 
rather  a  low  pressure  in  the  throat  of  the  nozzle,  but  in  general 
tests  on  the  flow  of  steam  show  a  pressure  in  the  throat  about 
equal  to  0.58  of  the  initial  pressure  provided  that  the  back  pres- 
sure has  less  than  ratio  3/5  to  the  initial  pressure;  this  corresponds 
with  Fliegner's  results  and  should  be  expected  from  his  com- 
parison with  molecular  velocity  on  page  430.  The  following 
table  gives  results  of  tests  made  by  Mr.  W.  H.  Kunhardt  *  in 
the  laboratories  of  the  Massachusetts  Institute  of  Technology: 

The  excess  of  the  throat  pressure  above  0.58  of  the  initial 

*  Transactions  Am.  Soc.  Mech.  Engs.,  vol.  xi,  p.  187. 


444 


FLOW  OF  FLUIDS 


pressure  for  the  tests  numbered  i  to  9  is  to  be  attributed  to  the 
excessive  length  of  the  tube.  Longer  tubes  tested  by  Biichner, 
showed  the  same  effect  in  an  exaggerated  degree. 

FLOW  OF  STEAM  THROUGH  SHORT  TUBES  WITH  ROUNDED 

ENTRANCES. 
Diameters  0-25  of  an  inch. 


Pressure  above  at- 
mosphere, pounds 
per  square  inch. 

Ratio  of 
absolute 
pressures. 

| 

Flow  in  pounds 
per  hour. 

1 

1 

j 

1 

c 

1 

0 

B 

d 

.9 

1 

u 

« 

i 

tsJS 

II 

.y  x. 

c    . 
JS  5 

gT 

e 

Length  of  tube, 

Duration,  minu 

Above  the  tube 

Below  the  tube. 

At  small  orifice 
side  of  tube. 

Barometer,  pou 
square  inch. 

Pressure  above 
tube  to  pressu 
below. 

Pressure  at  side 
orifice  to  pres 
above  tube. 

Temperature  of 
tube.  Fahrei 

Per  cent  of  moi 
steam  above  t 

8 

ft 
P 

Calculated  by 
Thermodynar 
equation  26 

Calculated  by  F 
kine's  equatic 

Coefficient  of  fli 
tion  (268). 

I 

i-5 

30 

74.1 

14.8 

41.2 

14.7 

0.332 

0.630 

126.2 

1.2 

221.0 

217.0 

224 

1.018 

2 

' 

30 

71.0 

13-2 

39-6 

14.8 

0.326 

0.634 

138-7 

i-5 

213.0 

207.8 

215 

1.025 

3 

20 

72.6 

19.7 

40.6 

14.7 

0-394 

0.634 

141.4 

0.5 

216.0 

211.4 

220 

1.022 

4 

20 

75-9 

20.4 

42.6 

14.7 

0.387 

0.632 

139-8 

0.7 

228.0 

219-3 

227 

1.040 

| 

20 

71.9 

24-5 

40.6 

14.7 

0.454 

0.638 

140.6 

0.7 

213.0 

209.7 

218 

1.  016 

6 

o  5 

30 

72.8 

14-8 

39-0 

14.8 

0.338 

0.614 

138.7 

0.3 

225.0 

213.6 

221 

1-053 

7 

20 

72.1 

20.4 

38-8 

14.8 

0.405 

0.61- 

142.2 

0.5 

223.5 

211.7 

219 

1.056 

8 

30 

72.6 

24.7 

39-o 

14.8 

0.452 

0.616 

144.0 

0.5 

223.0 

213-1 

220 

1.046 

c 

30 

73.1 

29.9 

39-2 

14.8 

0.509 

0.615 

145.2 

0.5 

225.5 

213.0 

222 

1.054 

10 

0.25 

30 

72.6 

24.8 

36.1 

14.9 

°-454 

0.583 

143-8 

0.4 

225.0 

2i3'5 

220 

1.054 

ii 

30 

72.6 

19.9 

36.1 

14.9 

0.398 

0.583 

141.6 

0.4 

225.0 

213-5 

220 

1.054 

12 

30 

72.7 

14.9 

36-2 

14.8 

o  339 

0.583 

140-5 

0.4 

227.0 

213.0 

220 

i.  066 

13 
14 

30 

30 

126.3 
125.0 

27.8 
40.8 

69.0 
67.9 

14-7 
14.7 

0.295 
0.398 

0.59^ 
0.5-J8 

155-0 
157-0 

0.5 

0.2 

358.8 

355-0 

338-9 
334-8 

355 

352 

1.058 
i.  060 

Design  of  a  Nozzle.  —  Required  the  dimensions  of  a  nozzle 
to  deliver  500  pounds  of  steam  per  hour  with  a  steam  pressure  of 
150  pounds  by  the  gauge  and  a  vacuum  of  26  inches  of  mercury. 
The  vacuum  of  26  inches  can  be  taken  as  substantially  equiva- 
lent to  2  pounds  absolute  and  the  steam  pressure  may  be  taken 
as  165  pounds  absolute.  The  throat  pressure  is  then  nearly 
96  pounds  absolute.  Assuming  the  steam  to  be  initially  dry, 
the  calculation  can  be  arranged  as  follows: 


+  #1  - 


6-  0- 


ri  +  ft 
ri  +  & 


=  784.4(1-0378  +0.5237  -0.4709)  =  855.5 

0,)-  585.7  (1.0378  +  0.5237-0.1753)  =811.8 

-  856.8  +  337.9  -  855.5  ~  295-4  =  43-8 
=  856.8  +  337.9  -  811.8  -  94.2  =  288.6. 


DESIGN  OF  A  NOZZLE  445 

The  quantities  just  obtained  are  the  amounts  of  heat  that 
would  be  available  for  producing  velocity  if  the  action  were 
adiabatic.  In  order  to  find  the  probable  velocity  allowing  for 
friction,  they  should  be  multiplied  by  i  —  y,  where  y  the  coeffi- 
cient for  friction  may  be  taken  as  0.15  for  the  determination  of 
the  exit  velocity  Vz.  As  for  the  throat  velocity,  there  are  two 
considerations,  the  friction al  effect  is  small  because  the  throat  is 
near  the  entrance,  and  all  experiments  indicate  that  orifices  and 
nozzles  which  are  not  unduly  long  deliver  the  full  amount  of 
steam  that  the  adiabatic  theory  indicates;  therefore  we  may 
make  the  calculation  for  that  part  of  the  nozzle  by  the  adiabatic 
method.  The  available  heats  for  producing  velocity  may  there- 
fore be  taken  as 

43.8  and  (i  —  0.15)  288.6=  245, 
and  the  velocities  are  therefore  (see  page  436) 


F2  =  V64.4  X  778  X  43.8=  1480. 


F3  =  V64.4  X  778  X  245  =  3500. 
The  quality  of  steam  in  the  throat  is 

*2  =  X2r2  +  r2=  855-5  -*-  889-9  =  °-961- 

To  find  the  quality  of  steam  at  the  exit  we  may  consider  that 
if  x3'  is  the  actual  quality  allowing  for  the  effect  of  friction  we 
have 

ri  +  ft  -  *a/rs  -  ft  =  245 
x»'=  (856.8  +  337.9  -  245  -  94.2)  -T-  1021.9  =  0.835. 

Though  not  necessary  for  the  solution  of  the  problem  it  is 
interesting  to  notice  that  adiabatic  expansion  to  the  exit  pressure 
would  give  for 

*3=*3r3  -*-',=  811.8  +  1021.9  =  0.795. 
Now  500  pounds  of  steam  an  hour  gives 
500  -T-  60  =  0.139 


446  FLOW  OF  FLUIDS 

of  a  pound  per  second;  consequently  the  areas  at  the  throat  and 
the  exit  will  be  by  equation  (268),  page  431,  in  square  inches 

144^2  =  144  X  0.139 

=  144  X  0.139  (0.961  X  4.583  +  0.616)  •*•  1480=  0.0597; 
144^3  =  144  X  0.139  (0.835  X  173.1  +  0.016)  •*-  3500  =  0.827. 
The  diameters  are,  therefore, 

d2  =  0.280  d3  =  1.026. 

If  the  taper  is  taken  to  be  one  in  ten,  the  conical  part  will  have 
a  length  of 

10  (1.026  —  0.280)  =  7.46  inches; 

and  allowing  for  the  rounding  at  the  entrance  and  for  a  fair  curve 
joining  the  throat  to  the  cone,  the  total  length  may  be  eight 
inches. 

A  nozzle  to  expand  steam  to  the  pressure  of  the  atmosphere 
only,  would  have  the  computation  for  the  exit  made  as  follows: 


+  6i~  *•  =  671.5  (1-0378  +  0-5237  -  0-3125)  -  838.7; 

ri  +  ft  -  x/3  -  &  =  856-8  +  337-9  -  838.7  -  180.3  =  175-7- 

Taking  the  coefficient  for  friction  as  o.io  the  available  heat 
appears  to  be  157.5  and  the  velocity  at  exit  will  be 

F3  =  V64-4  X  778  X  157.5  =  2810. 
The  quality  of  the  steam  comes  from  the  equation 

^i  +  ?1-^3-?3=I57-5- 

.'.  *,'  =  (856.8  +  337-9  -  157-5  ~  180.3)  +  969-7  =  0.884. 
The  area  at  the  exit  will  now  become 
144^3=  144  X  .139  (0.884  X  26.80  +  0.016)  -T-  2810=  0.169, 

and  the  corresponding  diameter  is  0.464  of  an  inch.  Taking 
the  taper  as  one  in  ten,  the  length  of  the  conical  part  of  the  nozzle 
becomes 

10  (0.464—  0.280)  =  1.84  inches, 

and  its  total  length  including  throat  and  inlet  may  be  2.3  inches. 


CHAPTER  XVIII. 
INJECTORS. 

AN  injector  is  an  instrument  by  means  of  which  a  jet  of  steam 
acting  on  a  stream  of  water  with  which  it  mingles,  and  by  which 
it  is  condensed,  can  impart  to  the  resultant  jet  of  water  a  sufficient 
velocity  to  overcome  a  pressure  that  may  be  equal  to  or  greater 
than  the  initial  pressure  of  the  steam.  Thus,  steam  from  a 
boiler  may  force  feed-water  into  the  same  boiler,  or  into  a  boiler 
having  a  higher  pressure.  The  mechanical  energy  of  the  jet  of 
water  is  derived  from  the  heat  energy  yielded  by  the  condensation 
of  the  steam-jet.  There  is  no  reason  why  an  injector  cannot  be 
made  to  work  with  any  volatile  liquid  and  its  vapor,  if  occasion 
may  arise  for  doing  so;  but  in  practice  it  is  used  only  for  forcing 
water.  An  essential  feature  in  the  action  of  an  injector  is  the 
condensation  of  the  steam  by  the  water  forced;  other  instruments 
using  jets  without  condensation,  like  the  water-ejector  in  which 
a  small  stream  at  high  velocity  forces  a  large  stream  with  a  low 
velocity,  differ  essentially  from  the  steam-injector. 

Method  of  Working.  —  A  very  simple  form  of  injector  is  shown 
by  Fig.  91,  consisting  of  three  essential  parts;  a,  the  steam-nozzle, 
6,  the  combining- tube,  and  c,  the  delivery-tube.  Steam  is  supplied 
to  the  injector  through  a  pipe  connected  at  d\  water  is  supplied 
through  a  pipe  at/,  and  the  injector  forces  water  out  through  the 
pipe  at  e.  The  steam-pipe  must  have  on  it  a  valve  for  starting 
and  regulating  the  injector,  and  the  delivery-pipe  leading  to  the 
boiler  must  have  on  it  a  check-valve  to  prevent  water  from  the 
boiler  from  flowing  back  through  the  injector  when  it  is  not 
working.  The  water-supply  pipe  commonly  has  a  valve  for 
regulating  the  flow  of  water  into  the  injector. 

This  injector,  known  as  a  non-lifting  injector,  has  the  water- 
reservoir  set  high  enough  so  that  water  will  flow  into  the  injector 

447 


448 


INJECTORS 


through  the  influence  of  gravity.  A  lifting  injector  has  a  special 
device  for  making  a  vacuum  to  draw  water  from  a  reservoir 
below  the  injector,  which  will  be  described  later. 

To  start  the  injector  shown  by  Fig.  91,  the  steam- valve  is  first 
opened  slightly  to  blow  out  any  water  that  may  have  gathered 
above  the  valve,  through  the  overflow,  since  it  is  essential  to  have 
dry  steam  for  starting.  The  steam-valve  is  then  closed,  and 
the  water- valve  is  opened  wide.  As  soon  as  water  appears  at  the 
overflow  between  the  combining-tube  and  the  delivery-tube  the 


FIG.  91. 


steam- valve  is  opened  wide,  and  the  jet  of  steam  from  the  steam- 
nozzle  mingles  with  and  is  condensed  by  the  water  and  imparts 
to  it  a  high  velocity,  so  that  it  passes  across  the  overflow  space 
between  the  combining-tube  and  the  delivery-tube  and  passes 
into  the  boiler.  When  the  injector  is  working  a  vacuum  is  liable 
to  be  formed  at  the  space  between  the  combining  and  delivery- 
tubes,  and  the  valve  at  the  overflow  closes  and  excludes  air 
which  would  mingle  with  the  water  and  might  interfere  with 
the  action  of  the  injector. 

Theory  of  the  Injector.  —  The  two  fundamental  equations  of 
the  theory  of  the  injector  are  deduced  from  the  principles  of  the 
conservation  of  energy  and  the  conservation  of  momenta. 


THEORY  OF  THE  INJECTOR  449 

The  heat  energy  in  one  pound  of  steam  at  the  absolute  pressure 
pl  in  the  steam-pipe  is 


where  rl  and  q^  are  the  heat  of  vaporization  and  heat  of  the  liquid 

corresponding  to  the  pressure  p^~  is  the  mechanical  equivalent 

A. 

of  heat  (778  foot-pounds),  and  xl  is  the  quality  of  the  steam;  if 
there  is  two  per  cent  of  moisture  in  the  steam,  then  x^  is  0.98. 

Suppose  that  the  water  entering  the  injector  has  the  tempera- 
ture /3,  and  that  its  velocity  where  it  mingles  with  the  steam  is  Vw'  ; 
then  its  heat  energy  per  pound  is 


and  its  kinetic  energy  is 


where  q3  is  the  heat  of  the  liquid  at  /3,  and  g  is  the  acceleration 
due  to  gravity  (32.2  feet). 

If  the  water  forced  by  the  injector  has  the  temperature  /4,  and 
if  the  velocity  of  the  water  in  the  smallest  section  of  the  delivery- 
tube  is  Vv,  then  the  heat  energy  per  pound  is 


and  the  kinetic  energy  is 


Let  each  pound  of  steam  draw  into  the  injector  y  pounds  of 
water;  then,  since  the  steam  is  condensed  and  forced  through 
the  delivery-tube  with  the  water,  there  will  be  i  +  y  pounds 
delivered  for  each  pound  of  steam.  Equating  the  sum  of  the 
heat  and  kinetic  energies  of  the  entering  steam  and  water  to  the 
sum  of  the  energies  in  the  water  forced  from  the  injector,  we 
have 


450  INJECTORS 

The  terms  depending  on  the  velocities  Vwf  and  Vw  are  never 
large  and  can  commonly  be  neglected. 

To  get  an  idea  of  the  influence  of  the  former,  we  may  consider 
that  the  pressure  forcing  water  into  a  non-lifting  injector  is  sel- 
dom, if  ever,  greater  than  the  pressure  of  the  atmosphere,  and 
the  corresponding  pressure  for  a  lifting  injector  is  always  less. 
Now,  the  pressure  of  the  atmosphere  is  equivalent  to  a  head  of 

hf  =  144  X  14.7  •*•  62.4  =  34  feet. 

A  liberal  estimate    of  y  (the    pounds  of  water  per  pound    of 
steam)  is  fifteen.     Therefore, 

y  '2 

y~^"'=  yh'  =  X5  X  34  =  510- 

In  order  that  an  injector  shall  deliver  water  against  the  steam- 
pressure  in  a  boiler  its  velocity  must  be  greater  than  would  be 
impressed  on  cold  water  by  a  head  equivalent  to  the  boiler- 
pressure.  Taking  the  boiler- pressure  at  250  pounds  by  the 
gauge,  or  265  pounds  absolute,  the  equivalent  head  will  be 

h  =  144  X  265  -r-  62.4  =  610  feet. 

Again  taking  fifteen"  for  y,  the  value  of  the  term  depending  on  Vw 
will  be 

(i  +  y)  ¥-*?-  =  (i  +  15)  610  =  9150. 

But  the  steam  supplied  to  an  injector  is  nearly  dry  and  at 
265  pounds  absolute 

rl  +  ql  =  826.2  +  379.6  =  1205.8, 

so  that  the  term  depending  on  that  quantity  will  have  the  value 
778  X  1206  =  939000. 

It  is,  therefore,  evident  that  the  term  depending  on  Vw  has 
an  influence  of  less  than  one  per  cent  and  that  the  term  depending 
on  VJ  can  be  entirely  neglected. 


THEORY  OF  THE  INJECTOR  451 

For  practical  purposes  we  may  calculate  the  weight  of  water 
delivered  per  pound  of  steam  by  the  equation 


This  equation  may  be  applied  to  any  injector  including  double 
injectors  with  two  steam-nozzles. 

The  discussion  just  given  shows  that  of  the  heat  supplied  to 
an  injector  only  a  very  small  part,  usually  less  than  one  per  cent, 
is  changed  into  work.  When  used  for  feeding  a  boiler,  or  for 
similar  purposes,  this  is  of  no  consequence,  because  the  heat 
not  changed  into  work  is  returned  to  the  boiler  and  there  is  no 
loss. 

For  example,  if  dry  steam  is  supplied  to  the  injector  at  120 
pounds  by  the  gauge  or  134.7  pounds  absolute,  if  the  supply- 
temperature  of  the  water  is  65°  F.,  and  if  the  delivery-temperature 
is  165°  F.,  then  the  water  pumped  per  pound  of  steam  is 

r.  +  q.  —  <74      860.0  +  321.  <  —  133.0 
y  =  _j  -  ft  -  24  =  _^LV  -  o  -  2  -  o^_  =  Ia 

&  -  &  133-°  -  33-  1 

From  the  conservation  of  energy  we  have  been  able  to  devise 
an  equation  for  the  weight  of  water  delivered  per  pound  of 
steam;  from  the  conservation  of  momenta  we  can  find  the  relation 
of  the  velocities. 

The  momentum  of  one  pound  of  steam  issuing  from  the  steam- 
nozzle  with  the  velocity  Vs  is  Vs  +  g',  the  momentum  of  y 
pounds  of  water  entering  the  combining-tube  with  the  velocity 
Vw'  is  yVwf  -r-  g]  and  the  momentum  of  i  +  y  pounds  of  water 
at  the  smallest  section  of  the  delivery-tube  is  (r  +  y)  Vw  -r-  g. 
Equating  the  sum  of  the  momenta  of  water  and  steam  before 
mingling  to  the  momentum  of  the  combined  water  and  steam 
in  the  delivery-tube, 

V.  +  yVw'-li+y)V.    ......     (271) 

This  equation  can  be  used  to  calculate  any  one  of  the  velocities 
provided  the  other  two  can  be  determined  independently.  Unfor- 


452  INJECTORS 

tunately  there  is  some  uncertainty  about  all  of  the  velocities  so 
that  the  proper  sizes  of  the  orifices  and  of  the  forms  and  propor- 
tions of  the  several  members  of  an  injector  have  been  determined 
mainly  by  experiment.  The  best  exposition  of  this  matter  is 
given  by  Mr.  Strickland  Kneass,*  who  has  made  many  experi- 
ments for  William  Sellers  &  Co.  The  practical  part  of  what 
follows  is  largely  drawn  from  his  work.  , 

Velocity  of  the  Steam-jet.  —  Equation  (269 )?  page  433,  gives 

i 


where  rl  and  ql  are  the  heat  of  vaporization  and  the  heat  of  the 
liquid  of  the  supply  of  steam  at  the  pressure  plt  and  rz  and  q2 
are  corresponding  quantities  at  the  pressure  p2  for  that  section 
of  the  tube  for  which  the  velocity  is  calculated;  x^  is  the  quality 
of  the  steam  at  the  pressure  p^  (usually  0.98  to  unity)  and  x2  is 
the  quality  at  the  pressure  p2  to  be  calculated  by  aid  of  the 
equation 


Here  Tl  and  T2  are  the  absolute  temperatures  corresponding  to 
the  pressures  pl  and  p2)  and  6l  and  02  are  the  entropies  of  the 

liquid  at  the  same  pressure.    Also  -  is  the  mechanical  equivalent 

A. 

of  heat  and  g  is  the  acceleration  due  to  gravity. 

Some  steam-nozzles  for  injectors  are  simple  converging  orifices 
and  others  have  a  throat  and  a  diverging  portion.  It  will  be 
found  in  all  cases  including  double  injectors,  that  the  pressure 
beyond  the  steam-  nozzle  is  less  than  half  the  pressure  causing 
the  flow,  and  consequently  the  pressure  at  the  narrowest  part 
of  the  steam-nozzle  and  also  the  velocity  at  that  place,  depend 
only  on  the  initial  pressure.  As  was  developed  in  the  preceding 
chapter,  the  pressure  and  velocity  at  any  part  of  an  expanding 
nozzle  depend  on  the  ratio  of  the  area  at  that  part  to  the  throat 
area,  and  are  consequently  under  control.  Also,  as  was  empha- 

*  Practice  and  Theory  of  the  Injector,  J.  Wiley  &  Sons. 


VELOCITY  OF  THE  STEAM-JET  453 

sized  by  Rosenhain's  experiments,  the  steam  will  expand  and 
gain  velocity  beyond  the  nozzle,  if  it  escapes  at  a  pressure  higher 
than  the  back-pressure.  For  an  injector  this  last  action  is 
influenced  by  the  fact  that  the  jet  from  the  steam-nozzle  mingles 
with  water  and  is  rapidly  condensed.  Some  injector  makers 
use  larger  tapers  than  those  recommended  in  the  preceding 
chapter  for  expanding  nozzles.  The  throat  pressure  may  be 
assumed  to  be  about  0.6  of  the  initial  pressure;  with  the  informa- 
tion in  hand  it  is  probably  not  worth  while  to  try  to  make  any 
allowance  for  friction. 

The  calculation  of  the  area  at  the  throat  of  a  steam  nozzle  by 
the  adiabatic  method  will  be  found  fairly  satisfactory;  the  calcu- 
lation of  the  final  velocity  of  the  steam  will  probably  not  be 
satisfactory,  as  complete  expansion  in  the  nozzle  seldom  takes 
place,  but  it  is  easy  to  show  that  the  velocity  is  sufficient  to 
account  for  the  action  of  the  instrument. 

For  example,  the  velocity  in  the  throat  of  a  nozzle  under  the 
pressure  of  120  pounds  by  the  gauge  or  134.7  pounds  absolute  is 

v  =  $  M  (~.  „  \  * 


(A.  \ 

=  {2  X  32.2  X  778  (869.9  -  0-965  X  899.2  +  321.1  -  282.9)}* 
=  1430  feet  per  second, 

having  for  x2 

'  +  6i  ~  #2)=  -4—  (I-°745  +  0.5035  -  0.4547) 


=  0-965, 
provided  that  p2  =  0.6^  =  80.8  pounds  absolute. 

If,  however,  the  pressure  at  the  exit  of  an  expanded  nozzle  is 
14.7  pounds  absolute,  then 

°'5°35  ~~  °-3I25)  =  0-877, 


1.4441 
and 

Fs=  1 2  X  32.2  X  778  (869.9  -  0-877  X  969.7  +  321.1  -  180.3)}* 
=  2860  feet  per  second, 


454  INJECTORS 

which  is  nearly  twice  that  just  calculated  for  the  velocity  at  the 
smallest  section  of  the  steam-nozzle.  Since  there  is  usually  a 
vacuum  beyond  the  steam-nozzle,  the  final  steam  velocity  is 
likely  to  be  considerably  larger,  but  this  computed  velocity  will 
suffice  for  explaining  the  dynamics  of  the  case. 

Velocity  of  Entering  Water.  —  The  velocity  of  the  water  in 
the  combining-tube  where  it  mingles  with  the  steam  depends  on 
(a)  the  lift  or  head  from  the  reservoir  to  the  injector,  (b)  the 
pressure  (or  vacuum)  in  the  combining-tube,  and  (c)  on  the 
resistance  which  the  water  experiences  from  friction  and  eddies 
in  the  pipe,  valves,  and  passages  of  the  injector.  The  first  of 
these  can  be  measured  directly  for  any  given  case;  for  example, 
where  a  test  is  made  on  an  injector.  In  determining  the  pro- 
portions of  an  injector  it  is  safe  to  assume  that  there  is  neither 
lift  nor  head  for  a  non-lifting  injector,  and  that  the  lift  for  a 
lifting-injector  is  as  large  as  can  be  obtained  with  certainty  in 
practice.  The  lift  for  an  injector  is  usually  moderate,  and 
seldom  if  ever  exceeds  20  feet. 

The  vacuum  in  the  combining-tube  may  amount  to  22  or  24 
inches  of  mercury,  corresponding  to  25  or  27  feet  of  water;  that 
is,  the  absolute  pressure  may  be  3  or  4  pounds  per  square  inch. 
The  vacuum  after  the  steam  and  water  are  combined  appears 
to  be  limited  by  the  temperature  of  the  water;  thus,  if  the  tem- 
perature is  165°  F.,  the  absolute  pressure  cannot  be  less  than 
5.3  pounds.  But  the  final  temperature  is  taken  in  the  delivery- 
pipe  after  the  water  and  condensed  steam  are  well  mixed  and  are 
moving  with  a  moderate  velocity. 

The  resistance  of  friction  in  the  pipes,  valves,  and  passages 
of  injectors  has  never  been  determined;  since  the  velocity  is  high 
the  resistance  must  be  considerable. 

If  we  assume  the  greatest  vacuum  to  correspond  to  27  feet  of 
water,  the  maximum  velocity  of  the  water  entering  the  combining- 
tube  will  not  exceed 


\/2gh  =  \/2  X  32.2  X  27  =  42   feet. 

If,  on  the  contrary,  the  effective  head  producing  velocity  is  as 
small  as  5  feet,  the  corresponding  velocity  will  be 


SIZES  OF  THE  ORIFICES  455 


2  X  32.2  X  5  =  18  feet. 

It  cannot  be  far  from  the  truth  to  assume  that  the  velocity  of 
the  water  entering  the  combining-tube  is  between  20  and  40 
feet  per  second. 

Velocity  in  the  Delivery-tube.  —  The  velocity  of  the  water  in 
the  smallest  section  of  the  delivery-tube  may  be  estimated  in  two 
ways;  in  the  first  place  it  must  be  greater  than  the  velocity  of 
cold  water  flowing  out  under  the  pressure  in  the  boiler,  and  in  the 
second  place  it  may  be  calculated  by  aid  of  equation  (271), 
provided  that  the  velocities  of  the  entering  steam  and  water  are 
determined  or  assumed. 

For  example,  let  it  be  assumed  that  the  pressure  of  the  steam 
in  the  boiler  is  120  pounds  by  the  gauge,  and  that,  as  calculated 
on  page  451,  each  pound  of  steam  delivers  10.5  pounds  of  water 
from  the  reservoir  to  the  boiler.  As  there  is  a  good  vacuum  in 
the  injector  we  may  assume  that  the  pressure  to  be  overcome  is 
132  pounds  per  square  inch,  corresponding  to  a  head  of 

132  X  144  , 

-^— 33  =  305  feet. 

62.4 

Now  the  velocity  of  water  flowing  under  the  head  of  305  feet  is 


\/2gh  =  "S/2  X  32.2  X  305  =  140  feet  per  second. 

The  velocity  of  steam  flowing  from  a  pressure  of  120  pounds 
by  the  gauge  through  a  diverging-tube  with  the  pressure  equal 
to  that  of  the  atmosphere  at  the  exit  has  been  calculated  to  be 
2830  feet  per  second.  Assuming  the  velocity  of  the  water  enter- 
ing the  combining-tube  to  be  20  feet,  then  by  equation  (271) 
we  have  in  this  case 

T/       Vs  +  yVw'      2860  -f  10.6  X  20  . 

Vw  = * = =  265  feet; 

i  +  y  i  +  10.6 

this  velocity  is  sufficient  to  overcome  a  pressure  of  about  470 
pounds  per  square  inch  if  no  allowance  is  made  for  friction  or 
losses. 

Sizes  of  the  Orifices.  —  From  direct  experiments  on  injectors  as 
well  as  from  the  discussion  in  the  previous  chapter,  it  appears 


456  INJECTORS 

that  the  quantity  of  steam  delivered  by  the  steam-nozzle  can  be 
calculated  in  all  cases  by  the  method  for  the  flow  of  steam, 
through  an  orifice,  assuming  the  pressure  in  the  orifice  to  be  T% 
of  the  absolute  pressure  above  the  orifice. 

Now  each  pound  of  steam  forces  y  pounds  of  water  from  the 
reservoir  to  the  boiler;  consequently  if  w  pounds  are  drawn  from 
the  reservoir  per  second  the  injector  will  use  w  -f-  y  pounds  of 
steam  per  second. 

The  specific  volume  of  the  mixture  of  water  and  steam  in  the 
smallest  section  of  the  steam-nozzle  is 
v2  =  x2u2  +  ff, 

where  oc2  is  the  quality,  u2  is  the  increase  of  volume  due  to  vapor- 
ization, and  cr  is  the  specific  volume  of  the  water.  The  volume 
of  steam  discharged  per  second  is 


y 

and  the  area  of  the  orifice  is 


where  Vs  is  the  velocity  at  the  smallest  section. 

For  example,  for  a  flow  from  134.7  pounds  absolute  to  80.8 
pounds  absolute  x2  is  0.965  and  Vs  is  1430  feet,  as  found  on 
page  453.  Again,  for  an  increase  of  temperature  from  65°  F. 
to  165°  F.,  the  water  per  pound  of  steam  is  10.6.  Calculating  the 
specific  volume  at  80.8  pounds,  we  have 

v2  =  x2u2  +  a=  0.965  (5.38  —  0.016)  +  0.016  =  5.23  cubic  feet. 

If  the  injector  is  required  to  deliver  1200  gallons  an  hour,  or 
I2QQ  X  231  X  62.4  _       _ 
1728  X  60  X  60 

pounds  per  second,  the  area  of  the  steam-nozzle  must  be 

wv7       2.78  X  S-2S  t 

as  =  —  2-  =  —  '  -  ^  —  •*•  =  o.oooo  so  square  feet. 
yVs      10.6  X  1430 

The  corresponding  diameter  is  0.420  of  an  inch,  or  10.6  milli- 
metres. 


SIZES  OF  THE  ORIFICES  457 

In  trying  to  determine  the  size  of  the  orifice  in  the  delivery- 
tube  we  meet  with  two  serious  difficulties:  we  do  not  know  the 
velocity  of  the  stream  in  the  smallest  section  of  the  delivery- 
tube,  and  we  do  not  know  the  condition  of  the  fluid  at  that  place. 
It  has  been  assumed  that  the  steam  is  entirely  condensed  by 
the  water  in  the  combining-tube  before  reaching  the  delivery- 
tube,  but  there  may  be  small  bubbles  of  uncondensed  steam  still 
mingled  with  the  water,  so  that  the  probable  density  of  the 
heterogeneous  mixture  may  be  less  than  that  of  water.  Since 
the  pressure  at  the  entrance  to  the  delivery-tube  is  small,  the 
specific  volume  of  the  steam  is  very  large,  and  a  fraction  of  a 
per  cent  of  steam  is  enough  to  reduce  the  density  of  the  steam 
to  one-half.  Even  if  the  steam  is  entirely  condensed,  the  air 
carried  by  the  water  from  the  reservoir  is  enough  to  sensibly 
reduce  the  density  at  the  low  pressure  (or  vacuum)  found  at  the 
entrance  to  the  delivery-tube. 

If  Vw  is  the  probable  velocity  of  the  jet  at  the  smallest  section 
of  the  delivery-tube,  and  if  d  is  the  density  of  the  fluid,  then  the 
area  of  the  orifice  in  square  feet  is 

w  (i  +  y)  . 

3»  =  -W' (274) 

for  each  pound  of  steam  mingles  with  and  is  condensed  by  y 
pounds  of  water  and  passes  with  that  water  through  the  delivery- 
tube;  w,  as  before,  is  the  number  of  pounds  of  water  drawn  from 
the  reservoir  per  second. 

For  example,  let  it  be  assumed  that  the  actual  velocity  in  the 
delivery-tube  to  overcome  a  boiler-pressure  of  120  pounds  by  the 
gauge  is  150  feet  per  second,  and  that  the  density  of  the  jet  is 
about  0.9  that  of  water;  then  with  the  value  of  w  =  2.78  and  y  = 
10.6,  we  have 

w(i  +  y)  2.78  X  n.6 

a>w  =  — T7    ,  '     = — —       — =  0.000361  sq.  ft. 

Vwdy          150  X  0.9  X  62.4  X  10.6 

The  corresponding  diameter  is  0.257  °f  an  mcn>  or  6.5  milli- 
metres. If  this  calculation  were  made  with  the  velocity  266 
(computed  for  expansion  to  atmospheric  pressure)  and  with 


458  INJECTORS 

clear  water  the  diameter  would  be  only  0.183  °f  an  inch;  this  is 
to  be  considered  rather  as  a  theoretic  minimum  than  as  a  prac- 
tical dimension. 

Steam-nozzle.  —  The  entrance  to  the  steam-nozzle  should  be 
well  rounded  to  avoid  eddies  or  reduction  of  pressure  as  the 
steam  approaches;  in  some  injectors,  as  the  Sellers'  injector, 
Fig.  92,  the  valve  controlling  the  steam  supply  is  placed  near 
the  entrance  to  the  nozzle,  but  the  bevelled  valve-seat  will  not 
interfere  with  the  flow  when  the  valve  is  open. 

It  has  already  been  pointed  out  that  the  steam-nozzle  may 
advantageously  be  made  to  expand  or  flare  from  the  smallest 
section  to  the  exit.  The  length  from  that  section  to  the  end  may 
be  between  two  and  three  times  the  diameter  at  that  section. 

Consider  the  case  of  a  steam-nozzle  supplied  with  steam  at 
120  pounds  boiler-pressure:  it  has  been  found  that  the  velocity 
at  the  smallest  section,  on  the  assumption  that  the  pressure  is 
then  80.8  pounds,  is  1430  feet  per  second,  and  that  the  specific 
volume  is  5.23  cubic  feet.  If  the  pressure  in  the  nozzle  is 
reduced  to  14.7  pounds,  at  the  exit,  the  velocity  becomes  2860 
feet  per  second,  the  quality  being  oc2  =  0.877.  The  specific 
volume  is  consequently 

V2  =  X2u2  +  a=  0.877  (26.78  —  0.016)  +  0.016=  23.5  cu.  ft. 

The  areas  will  be  directly  as  the  specific  volumes  and  inversely 
as  the  velocities,  so  that  for  this  case  we  shall  have  the  ratio  of 
the  areas 

5.23:  23.5  )=i         ' 
2860:  1430$ 

and  the  ratio  of  the  diameter  will  be 

Vi  •  \/2725  =  i  :  1.5. 

Combining- tube.  —  There  is  great  diversity  with  different 
injectors  in  the  form  and  proportions  of  the  combining-tube. 
It  is  always  made  in  the  form  of  a  hollow  converging  cone, 
straight  or  curved.  The  overflow  is  commonly  connected  to  a 
space  between  the  combining-tube  and  the  delivery- tube;  it  is, 


EFFICIENCY  OF  THE  INJECTOR  459 

however,  sometimes  placed  beyond  the  delivery-tube,  as  in  the 
Sellers'  injector,  Fig.  92.  In  the  latter  case  the  combining-  and 
delivery-tubes  may  form  one  continuous  piece,  as  is  seen  in  the 
double  injector  shown  by  Fig.  93. 

The  Delivery-tube.  —  This  tube  should  be  gradually  enlarged 
from  its  smallest  diameter  to  the  exit  in  order  that  the  water  in  it 
may  gradually  lose  velocity  and  be  less  affected  by  the  sudden 
change  of  velocity  where  this  tube  connects  to  the  pipe  leading 
to  the  boiler. 

It  is  the  custom  to  rate  injectors  by  the  size  of  the  delivery- 
tube;  thus  a  No.  6  injector  may  have  a  diameter  of  6  mm.  at 
the  smallest  section  of  the  delivery-tube. 

Mr.  Kneass  found  that  a  delivery-tube  cut  off  short  at  the 
smallest  section  would  deliver  water  against  35  pounds  pressure 
only,  without  overflowing;  the  steam- pressure  being  65  pounds. 
A  cylindrical  tube  four  times  as  long  as  the  internal  diameter, 
under  the  same  conditions  would  deliver  only  against  24  pounds. 
A  tube  with  a  rapid  flare  delivered  against  62  pounds,  and  a 
gradually  enlarged  tube  delivered  against  93  pounds. 

If  the  delivery-tube  is  assumed  to  be  filled  with  water  without 
any  admixture  of  steam  or  air,  then  the  relative  velocities  at 
different  sections  may  be  assumed  to  be  inversely  proportional 
to  the  corresponding  areas.  This  gives  a  method  of  tracing  the 
change  of  velocity  of  the  water  in  the  tube  from  its  smallest 
diameter  to  the  exit. 

A  sudden  change  in  the  velocity  is  very  undesirable,  as  at  the 
point  where  the  change  occurs  the  tube  is  worn  and  roughened, 
especially  if  there  are  solid  impurities  in  the  water.  It  has  been 
proposed  to  make  the  form  of  the  tube  such  that  the  change  of 
velocity  shall  be  uniform  until  the  pressure  has  fallen  to  that  in 
the  delivery-pipe;  but  this  idea  is  found  to  be  impracticable,  as 
it  leads  to  very  long  tubes  with  a  very  wide  flare  at  the  end. 

Efficiency  of  the  Injector.  —  The  injector  is  used  for  feeding 
boilers,  and  for  little  else.  Since  the  heat  drawn  from  the  boiler 
is  returned  to  the  boiler  again,  save  the  very  small  part  which 
is  changed  into  mechanical  energy,  it  appears  as  though  the 


460 


INJECTORS 


efficiency  was  perfect,  and  that  one  injector  is  as  good  as  another 
provided  that  it  works  with  certainty.  We  may  almost  consider 
the  injector  to  act  as  a  feed-water  heater,  treating  the  pumping 
in  of  feed-water  as  incidental.  It  has  already  been  pointed  out 


FIG.  92- 

on  page  450  that  the  kinetic  energy  of  the  jet  in  the  delivery- 
tube  is  less  than  one  per  cent  of  the  energy  due  to  the  condensa- 
tion of  the  steam.  On  this  account  the  injector  is  used  wherever 
cold  water  must  be  forced  into  a  boiler,  as  on  a  locomotive,  or 
when  sea-water  is  supplied  to  a  marine  boiler.  Considering 
only  the  advantage  of  supplying  hot  water  to  the  boiler,  it 
almost  seems  as  though  the  more  steam  a*n  injector  uses  the 
better  it  is.  Such  a  view  is  erroneous,  as  it  is  often  desirable 
to  supply  water  without  immediately  reducing  the  steam- 
pressure  and  then  it  is  necessary  to  use  as  little  steam  as  may  be. 
It  is,  however,  true  that  simplicity  of  construction  and  certainty 
of  action  are  of  the  first  importance  in  injectors. 

Lifting  Injector.  —  The  injector  described  at  the  beginning  of 


DOUBLE  INJECTORS  461 

this  chapter  was  placed  so  that  water  from  the  reservoir  would 
run  in  under  the  influence  of  gravity.  When  the  injector  is 
placed  higher  than  the  reservoir  a  special  device  is  provided  for 
lifting  the  water  to  start  the  injector.  Thus  in  the  Sellers' 
injector,  Fig.  92,  there  is  a  long  tube  which  protrudes  well  into 
the  combining-tube  when  the  valves  w  and  x  are  both  closed. 
When  the  rod  B  is  drawn  back  a  little  by  aid  of  the  lever  H  the 
valve  w  is  opened,  admitting  steam  through  a  side  orifice  to  the 
tube  mentioned.  Steam  from  this  tube  drives  out  the  air  in 
the  injector  through  the  overflow,  and  water  flows  up  into  the 
vacuum  thus  formed,  and  is  itself  forced  out  at  the  overflow. 
The  starting-lever  H  is  then  drawn  as  far  back  as  it  will  go, 
opening  the  valve  x  and  supplying  steam  to  the  steam-nozzle. 
This  steam  mingles  with  and  is  condensed  by  the  water  and 
imparts  to  the  water  sufficient  velocity  to  overcome  the  boiler- 
pressure.  Just  as  the  lever  H  reaches  its  extreme  position  it 
closes  the  overflow  valve  K  through  the  rod  L  and  the  crank  at  R. 

Since  lifting-injectors  may  be  supplied  with  water  under  a 
head,  and  since  a  non-lifting  injector  when  started  will  lift 
water  from  a  reservoir  below  it,  or  may  even  start  with  a  small 
lift,  the  distinction  between  them  is  not  fundamental. 

Double  Injectors.  —  The  double  injector  illustrated  by  Fig.  93, 
which  represents  the  Korting  injector,  consists  of  two  complete 
injectors,  one  of  which  draws  water  from  the  reservoir  and 
delivers  it  to  the  second,  which  in  turn  delivers  the  water  to  the 
boiler.  To  start  this  injector  the  handle  A  is  drawn  back  to 
the  position  B  and  opens  the  valve  supplying  steam  to  the 
lifting- injector.  The  proper  sequence  in  opening  the  valves 
is  secured  by  the  simple  device  of  using  a  loose  lever  for  joining 
both  to  the  valve-spindle;  for  under  steam-pressure  the  smaller 
will  open  first,  and  when  it  is  open  the  larger  will  move.  The 
steam-nozzle  of  the  lifter  has  a  good  deal  of  flare,  which  tends 
to  form  a  good  vacuum.  The  lifter  first  delivers  water  out  at 
the  overflow  with  the  starting  lever  at  5;  then  that  lever  is  pulled 
as  far  as  it  will  go,  opening  the  valve  for  the  second  injector  or 
forcer,  and  closing  both  overflow  valves. 


462 


INJECTORS 


Self-adjusting  Injectors.  —  In  the  discussions  of  injectors 
thus  far  given  it  has  been  assumed  that  they  work  at  full  capac- 
ity, but  as  an  injector  must  be  able  to  bring  the  water-level 
in  a  boiler  up  promptly  to  the  proper  height,  it  will  have  much 
more  than  the  capacity  needed  for  feeding  the  boiler  steadily. 
Any  injector  may  be  made  to  work  at  a  reduced  capacity  by 
simply  reducing  the  opening  of  the  steam-valve,  but  the  limit 


FIG.  93. 


of  its  action  is  soon  reached.  The  limit  may  be  extended  some- 
what by  partially  closing  the  water-supply  valve  and  so  limiting 
the  water-supply. 

The  original  Giffard  injector  had  a  movable  steam-nozzle  to 
control  the  thickness  of  the  sheet  of  water  mingling  with  the 
steam,  and  also  had  a  long  conical  valve  thrust  into  the  steam- 
nozzle  by  which  the  effective  area  of  the  steam- jet  could  be  regu- 
lated. Thus  both  water  and  steam  passages  could  be  controlled 
without  changing  the  pressures  under  which  they  were  supplied, 
and  the  injector  could  be  regulated  to  work  through  a  wide 
range  of  pressures  and  capacities.  The  main  objection  was 
that  the  injector  was  regulated  by  hand  and  required  much 
attention. 


SELF-ADJUSTING  INJECTORS  463 

In  the  Sellers'  injector,  Fig.  92,  the  regulation  of  the  steam- 
supply  by  a  long  cone  thrust  through  the  steam-nozzle  is 
retained,  but  the  supply  of  water  is  regulated  by  a  movable 
combining-tube,  which  is  guided  at  each  end  and  is  free  to  move 
forwards  and  backwards.  At  the  rear  the  combining-tube  is 
affected  by  the  pressure  of  the  entering  water,  and  in  front  it  is 
subjected  to  the  pressure  in  the  closed  space  O,  which  is  in 
communication  with  the  overflow  space  between  the  combining- 
tube  and  the  delivery-tube,  in  this  injector  the  space  is  only  for 
producing  the  regulation  of  the  water-supply  by  the  motion  of 
the  combining-tube,  as  the  actual  overflow  is  beyond  the 
delivery-tube  at  K.  When  the  injector  is  running  at  any  regular 
rate  the  pressures  on  the  front  and  the  rear  of  the  combining-tube 
are  nearly  equal,  and  it  remains  at  rest.  When  the  starting- 
lever  is  drawn  out  or  the  steam-pressure  increases,  the  inflowing 
steam  is  not  entirely  condensed  in  the  combining-tube  as  it  is 
during  efficient  action;  lateral  contraction  of  the  jet  therefore 
occurs  when  crossing  the  overflow  chamber,  causing  a  reduction 
of  pressure  in  O,  which  causes  the  tube  to  move  toward  D  and 
increase  the  supply  of  water.  When  the  starting-lever  is  pushed 
inward,  reducing  the  flow  of  steam,  the  impulsive  effort  is 
insufficient  to  force  a  full  supply  of  water  through  the  delivery- 
tube,  and  there  is  an  overflow  into  the  chamber  O  which  pushes 
the  combining-tube  backwards  and  reduces  the  inflow  of  water. 
The  injector  is  always  started  at  full  capacity  by  pulling  the 
steam-valve  wide  open,  as  already  described;  after  it  is  started 
the  steam-supply  is  regulated  at  will  by  the  engineer  or  boiler 
attendant,  and  the  water  is  automatically  adjusted  by  the  movable 
combining-tube,  and  the  injector  will  require  attention  only 
when  a  change  of  the  rate  of  feeding  the  boiler  is  required  on 
account  of  either  a  change  in  the  draught  of  steam  from  the 
boiler,  or  a  change  of  steam-pressure,  for  the  capacity  of  the 
injector  increases  with  a  rise  of  pressure. 

A  double  injector,  such  as  that  represented  by  Fig.  93,  is  to  a 
certain  extent  self-adjusting,  since  an  increase  of  steam-pressure 
causes  at  once  an  increase  in  the  amount  of  water  drawn  in  by 


464 


INJECTORS 


the  lifter  and  an  increase  in  the  flow  of  steam  through  the  steam- 
nozzle  of  the  forcer.  Such  injectors  have  a  wide  range  of  action 
and  can  be  controlled  by  regulating  the  valve  on  the  steam- 
pipe. 

Restarting  Injectors.  —  If  the  action  of  any  of  the  injector 
thus  far  described  is  interrupted  for  any  reason,  it  is  necessary  to 

shut  off  steam  and  start  the 
injector  anew;  sometimes  the 
injector  has  become  heated 
while  its  action  is  interrupted, 
and  there  may  be  difficulty  in 
starting.  To  overcome  this 
difficulty  various  forms  of 
restarting  injectors  have  been 
devised,  such  as  the  Sellers, 
Fig.  94.  This  injector  has 
four  fixed  nozzles  in  line,  the 
steam-nozzle  3,  the  draft-tube 
n,  the  combining-tube  2, 
and  the  delivery-tube  at  the 
bottom.  There  is  also  a  slid- 
ing bushing  5  and  an  overflow 

valve  15.  The  steam-nozzle  has  a  wide  flare  and  makes  a  vacuum 
which  draws  water  from  the  supply- tank  under  all  conditions;  the 
water  passes  through  the  draught-tube  and  out  at  the  overflow 
until  the  condensation  of  steam  in  the  combining-tube  makes  a 
partial  vacuum  that  draws  up  the  bushing  5  against  the  draught- 
tube  and  shuts  off  the  passage  to  the  overflow;  the  injector  then 
forces  water  to  the  boiler.  If  the  injector  stops  for  any  cause 
the  bushing  falls  and  the  injector  takes  the  starting  position  and 
will  start  as  soon  as  supplied  with  water  and  steam. 

Self-acting  Injector.  —  The  most  recent  type  of  Sellers'  injector, 
invented  by  Mr.  Kneass  and  represented  by  Fig.  95  is  both  self- 
starting  and  self-adjusting.  It  is  a  double  injector  with  all  the  jets 
in  one  line;  a,  b,  and  c  are  the  steam-nozzle,  the  combining-tube, 
and  the  delivery-tube  of  the  forcer;  the  lifter  is  composed  of  the 


FIG.  94. 


OF    THE 

UNIVERSITY 


TYI 


INJECTORS 


465 


466  INJECTORS 

annular  steam-nozzle  d,  and  the  annular  delivery-tube  e,  sur- 
rounding the  nozzle  a.  The  proportions  are  such  that  the  lifter 
can  always  produce  a  suction  in  the  feed-pipe  even  when  there 
is  a  discharge  from  the  main  steam-nozzle,  and  it  is  this  fact 
that  establishes  the  restarting  feature.  When  the  feed-water 
rises  to  the  tubes  it  meets  the  steam  from  the  lifter-nozzle  and 
is  forced  in  a  thin  sheet  and  with  high  velocity  into  the  combining- 
tube  of  the  forcer,  where  it  comes  in  contact  with  the  main 
steam- jet,  a'nd  mingling  with  and  condensing  it,  receives  a 
high  velocity  which  enables  it  to  pass  the  overflow  orifices  and 
proceed  through  the  delivery-tube  to  the  boiler. 

Like  any  double  injector,  the  lifter  and  forcer  have  a  con- 
siderable range  of  action  through  which  the  water  is  adjusted 
to  the  steam-supply;  but  there  is  a  further  adjustment  in  this 
injector,  for  when  a  good  vacuum  is  established  in  the  space 
surrounding  the  combining-tube,  water  can  enter  through  the 
check- val ve /,  and  flowing  through  the  orifices  in  the  combin- 
ing-tube mingles  with  the  jet  in  it,  and  is  forced  with  that  jet 
into  the  boiler. 

The  steam-valve  is  seated  on  the  end  of  the  lifter-nozzle, 
and  it  has  a  protruding  plug  which  enters  the  forcer-nozzle. 
When  the  valve  is  opened  to  start  the  injector,  steam  is  sup- 
plied first  to  the  starter,  and  soon  after,  by  withdrawing  the 
plug,  to  the  forcer.  If  the  steam  is  dry  the  starting-lever 
may  be  moved  back  promptly;  if  there  is  condensed  water  in 
the  steam-pipe,  the  starting-handle  should  be  moved  a  little 
way  to  first  open  the  valve  of  the  lifter,  and  then  it  is  drawn 
as  far  back  as  it  will  go,  as  soon  as  water  appears  at  the  over- 
flow. The  water-supply  may  be  regulated  by  the  valve  g, 
which  can  be  rotated  a  part  of  a  turn.  The  minimum  delivery 
of  the  injector  is  obtained  by  closing  this  valve  till  puffs  of 
steam  appear  at  the  overflow,  and  then  opening  it  enough 
to  stop  the  escape  of  steam. 

When  supplied  with  cold  water  this  injector  wastes  very 
little  in  starting.  If  the  injector  is  hot  or  is  filled  with  hot 
water  when  started,  it  will  waste  hot  water  till  the  injector  is 


EXHAUST  STEAM  INJECTORS 


467 


*L>WA\JST 


cooled  by  the  water  from  the  feed-  supply,  and  will  then  work 
as  usual.  If  air  leaks  into  the  suction-pipe  or  if  there  is  any 
other  interference  with  the  normal  action,  the  injector  wastes 
water  or  steam  till  normal  conditions  are  restored,  when  it 
starts  automatically. 

Exhaust  Steam  Injectors.  —  Injectors  supplied  with  ex- 
haust-steam from  a  non-condensing  engine  can  be  used  to 
feed  boilers  up  to  a  pressure  of  about  80  pounds.  Above 
this  pressure  a  supplemental  jet  of  steam  from  the  boiler  must 
be  used.  Such  an  injector,  as  made  by  Schaffer  and  Buden- 
berg,  is  represented  by  Fig.  96;  when 
used  with  low  boiler-pressure  this  in- 
jector has  a  solid  cone  or  spindle  in- 
stead of  the  live-steam  nozzle.  To 
provide  a  very  free  overflow  the  com-  jjj 
bining-tube  is  divided,  and  one  side  is  £ 
hung  on  a  hinge  and  can  open  to  give 
free  exit  to  the  overflow  when  the 
injector  is  started.  When  the  injector 
is  working  it  closes  down  into  place. 
The  calculation  for  an  exhaust-steam 
injector  shows  that  enough  velocity 
may  be  imparted  to  the  water  in  the 
delivery-tube  to  overcome  a  moderate 
boiler-pressure. 

For  example,  an  injector  supplied  with  steam  at  atmospheric 
pressure,  and  raising  the  feed-water  from  65°  F.  to  145°  F., 
will  draw  from  the  reservoir 


1  4-  180.3  —  113-0  _ 
113.0  -  33.1 


FIG.  96. 


04-  & 


pounds  of  water  per  pound  of  steam.  In  this  case  as  the  steam- 
nozzle  is  converging  we  will  use  for  computing  the  velocity  the 
pressure 

0.6  X  14.7  =  8.8  pounds. 


468 


INJECTORS 


This  will  give 

+01  ~  #2)  =  646.7  (1.4441  +0.3125  -.2745)  =958.6, 


consequently 


=  \/2  X  32.2  X  778  (969.7  +  180.3  -  95^.6  -  155.3  =  J34o. 

Assuming  the  velocity  of  the  water  entering  the  combining- 
tube  will  give  for  the  velocity  of  the  jet  in  the  combining-tube 

,,       1340  +  13.0  X  30  , 

Vw=-*2-1  -  -  -  —   =  124  feet. 
i  +  13.0 

This  velocity  is  equivalent  to  that  produced  by  a  static  pressure 

of 

I242  X  62.4 

=  I03 
64.4  X  144 

pounds  absolute,  or  a  gauge  pressure  of  88  pounds.  No  allow- 
ance is  made  for  reduction  of  density  by  bubbles  of  steam  in 
the  combining-tube  or  for  resistance  of  pipes  and  valves.  If 


FIG.  97- 


such  an  injector  can  take  advantage  of  further  expansion  either 
in  the  steam-nozzle  or  beyond,  the  velocity  may  be  greater  than 
that  computed  and  a  better  action  might  ensue. 
Unless  the  exhaust-steam  is  free  from  oil  its  use  for  feeding 


WATER-EJECTOR  469 

the  boiler  with  an  exhaust-steam  injector  will  result  in  fouling 
the  boiler. 

Water-ejector.  —  Fig.  97  represents  a  device  called  a  water- 
ejector,  in  which  a  small  stream  of  water  in  the  pipe  M  flowing 
from  the  reservoir  R  raises  water  from  the  reservoir  R"  to  the 
reservoir  R'. 

Let  one  pound  of  water  from  the  reservoir  R  draw  y  pounds 
from  R",  and  deliver  -i  +  y  pounds  to  R1 '.  Let  the  velocity  of 
the  water  issuing  from  A  be  v\  that  of  the  water  entering  from 
R"  be  v2  at  N',  and  that  of  the  water  in  the  pipe  O  be  vr  The 
equality  of  momenta  gives 

v  +  yv,  =  (i  +  y)  vl (275) 

Let  x  be  the  excess  of  pressure  at  M  above  that  at  AT  expressed 
in  feet  of  water;  then 

v*  =  2gx; 

v2   =  2g  (H  +  x); 

V?   =   2g  (h   +  X) 

Substituting  in  equation  (275), 

+  x  +  y  Vx  =  (i  +  y) 


•VA+?       .     .     .   (276) 


+  x  - 

It  is  evident  from  inspection  of  the  equation  (276)  that  y 
may  be  increased  by  increasing  x\  for  example,  by  placing  the 
injector  above  the  level  of  the  reservoir  so  that  there  may  be  a 
vacuum  in  front  of  the  orifice  A. 

s~< 

If  the  weight  G  of  water  is  to  be  lifted  per  second,  then  - 
pounds  per  second  must  pass  the  orifice  A,  G  pounds  the  space 
at  N,  and  li  +  -J  G  pounds  through  the  section  at  O;  which, 

with  the  several  velocities  v,  vv  and  vv  give  the  data  for  the 
calculation  of  the  required  areas. 

PROBLEM.  —  Required    the    calculation    for    a    water-ejector 


470  INJECTORS 

to  raise  1200  gallons  of  water  an  hour,  H  =  96  ft.,  h  =  12  ft., 

x  =  4  ft. 

Vx  =  V4  =  2;  VjEZ"  +  x=  \/ioo  =  10;  Vh  +  #  =  \/i6  =  4; 


The  velocities  are 


v    =  V2  X  32.2  X  100  =  80.25  feet  per  second; 
vl  =\/2  X  32.2  X  16     =  32.10  feet  per  second; 


v2  =\/2  X  32.2  X  4      =  16.05  feet  Per  second. 
1200  gallons  an  hour  =  0.04452  cubic  feet  per  second. 
The  areas  are 

0.04452  . 

a   _  -  :m  —      =  0.000185  square  feet; 
3  X  80.25 


4  X  0.04452 
=  2 ±±3_  =  0.06185    square  feet; 


0.04452 

T^  =  0.00277    square  feet. 

The  diameters  corresponding  to  the  velocities  v  and  v,  are 
d   =  0.18  of  an  inch; 
d^  =  0.58  of  an  inch. 

The  area  a2  is  of  annular  form,  having  the  area  0.4  of  a  square 
inch. 

Ejector.  —  When  the  ejector  is  used  for  raising  water  where 
there  is  no  advantage  in  heating  the  water,  it  is  a  very  wasteful 
instrument.  The  efficiency  is  much  improved  by  arranging 

the    instrument    as    in   Fig.    98,  so 
~  that  the  steam-nozzle  A  shall  deliver 

a  small  stream  of  water  at  a  high 

velocity,    which,   as    in    the  water- 
ejector,  delivers  a  larger  stream  at 

a  less  velocity.  Each  additional  conical  nozzle  increases  the 
quantity  at  the  expense  of  the  velocity,  so  that  a  large  quantity 
of  water  may  be  lifted  a  small  height. 


EJECTOR-CONDENSERS  471 

Ejectors  are  commonly  fitted  in  steamships  as  auxiliary  pumps 
in  case  of  leakage,  a  service  for  which  they  are  well  fitted,  since 
they  are  compact,  cheap,  and  powerful,  and  are  used  only  in 
emergency,  when  economy  is  of  small  consequence. 

Ejector-condensers.  —  When  there  is  a  good  supply  of  cold 
condensing  water,  an  exhaust-steam  ejector,  using  all  the 
steam  from  the  engine,  may  be  arranged  to  take  the  place  of 
the  air-pump  of  a  jet-condensing  engine.  The  energy  of  the 
exhaust-steam  flowing  from  the  cylinder  of  the  engine  to  the 
combining-tube,  where  the  absolute  pressure  is  less  and  where 
the  steam  is  condensed,  is  sufficient  to  eject  the  water  and  the  air 
mingled  with  it  against  the  pressure  of  the  atmosphere,  and  thus 
to  maintain  the  vacuum. 

For  example,  if  the  absolute  pressure  in  the  exhaust-pipe  is  2 
pounds,  and  if  the  temperatures  of  the  injection  and  the  delivery 
are  50°  F.  and  97°  F.,  then  the  water  supplied  per  pound  of 
steam  will  be  about  22  pounds.  If  the  pressure  at  the  exit  of 
the  steam-nozzle  can  be  taken  as  one  pound  absolute,  the  velocity 
of  the  steam- jet  will  be  1490  feet  per  second.  If  the  water  is 
assumed  to  enter  with  a  velocity  of  20  feet,  the  velocity  of  the 
water- jet  in  the  combining-tube  will  be  84  feet,  which  can  over- 
come a  pressure  of  48  pounds  per  square  inch. 


CHAPTER  XIX. 

STEAM-TURBINES. 

THE  recent  rapid  development  of  steam-turbines  may  be 
attributed  largely  to  the  perfecting  of  mechanical  construction, 
making  it  possible  to  construct  large  machinery  with  the  accuracy 
required  for  the  high  speeds  and  close  adjustments  which  these 
motors  demand. 

An  adequate  treatment  of  steam-turbines,  including  details  of 
design,  construction,  and  management,  would  require  a  separate 
treatise;  but  there  is  an  advantage  in  discussing  here  the  thermal 
problems  that  arise  in  the  transformation  of  heat  into  kinetic 
energy,  and  the  application  of  this  energy  to  the  moving  parts 
of  the  turbine.  For  this  purpose  it  is  necessary  to  give  attention 
to  the  action  of  jets  of  fluids  on  vanes  and  to  the  reaction  of  jets 
issuing  from  moving  orifices,  subjects  that  otherwise  would 
appear  foreign  to  this  treatise. 

The  fundamental  principles  of  the  theory  of  turbines  are  the 
same  whether  they  are  driven  by  water  or  by  steam;  but  the  use 
of  an  elastic  fluid  like  steam  instead  of  a  fluid  like  water,  which 
has  practically  a  constant  density,  leads  to  differences  in  the 
application  of  those  principles.  One  feature  is  immediately 
evident  from  the  discussion  of  the  flow  of  fluids  in  Chapter  XVII, 
namely,  that  exceedingly  high  velocities  are  liable  to  be  devel- 
oped. Thus,  on  page  444  it  was  found  that  steam  flowing  from 
a  gauge  pressure  of  150  pounds  per  square  inch  into  a  vacuum 
of  26  inches  of  mercury  (2  pounds  absolute)  through  a  proper 
nozzle,  developed  a  velocity  of  3500  feet  per  second,  with  an 
allowance  of  0.15  for  friction.  This  range  of  pressure  corre- 
sponds to  a  hydraulic  head  of 

163  X  144  -*-  62.4  =  376   feet; 
472 


IMPULSE  473 

and  such  a  head  will  give  a  velocity  of 

V  =  \/2  X  32.2  X  376  =  156  feet  per  second. 

But  so  great  a  hydraulic  head  or  fall  of  water  is  seldom,  if  ever, 
applied  to  a  single  turbine,  and  would  be  considered  inconvenient. 
One  hundred  feet  is  a  large  hydraulic  head,  yielding  a  velocity 
of  80  feet  per  second,  and  twenty-five  feet  yielding  a  velocity  of 
40  feet  per  second  is  considered  a  very  effective  head. 

If  heads  of  300  feet  and  upward  were  frequent,  it  is  likely 
that  compound  turbines  would  be  developed  to  use  them;  except 
for  relatively  small  powers,  steam-turbines  are  always  compound, 
that  is,  the  steam  flows  through  a  succession  of  turbines  which 
may  therefore  run  at  more  manageable  speeds. 

The  great  velocities  that  are  developed  in  steam  turbines, 
even  when  compounded,  require  careful  reduction  of  clearances, 
and  although  they  are  restricted  to  small  fractions  of  an  inch 
the  question  of  leakage  is  very  important.  Another  feature  in 
which  steam  turbines  differ  from  hydraulic  turbines  is  that 
steam  is  an  elastic  fluid  which  tends  to  fill  any  space  to  which  it 
is  admitted.  The  influence  of  this  feature  will  appear  in  the 
distinction  between  impulse  and  reaction  turbines. 

Impulse.  —  If  a  well  formed  stream  of  water  at  moderate 
velocity  flows  from  a  conical  nozzle,  on  a  flat  plate  it  spreads 
over  it  smoothly  in  all  directions  and  exerts  a 
steady  force  on  it.  If  the  velocity  of  the  stream 
is  V1  feet  per  second,  and  if  w  pounds  of  water  are 
discharged  per  second,  the  force  will  be  very 

FIG.  99. 

nearly  equal  to 

"I'-' 

Here  we  have  the  velocity  in  the  direction  of  the  jet  changed 
from  V1  feet  per  second  to  zero;  that  is,  there  is  a  retardation,  or 
negative  acceleration,  of  V1  feet  per  second;  consequently  the 
force  is  measured  by  the  product  of  mass  and  the  acceleration, 
g  being  the  acceleration  due  to  gravity.  A  force  exerted  by  a 
jet  or  stream  of  fluid  on  a  plate  or  vane  is  called  an  impulse.  It 


H 


474 


STEAM-TURBINES 


is  important  to  keep  clearly  in  mind  that  we  are  dealing  with 
velocity,  change  of  velocity  or  acceleration,  and  force,  and  that 
the  force  is  measured  in  the  usual  way.  The  use  of  a  special 
name  for  the  force  which  is  developed  in  this  way  is  unfortunate 
but  it  is  too  well  established  to  be  neglected. 

If  the  plate  or  vane,  instead  of  remaining  at  rest,  moves  with 
the  velocity  of  V  feet  per  second,  the  change  in  velocity  or  negative 
acceleration  will  be  V1  —  V  feet  per  second,  and  the  force  or 
impulse  will  be 


This  force  in  one  second  will  move  the  distance  V  feet  and  will 
do  the  work 

™(Fl-  F)F=  y  (VtV-  F2)  .     .    .  (276) 

o  o 

foot-pounds. 

Since  the  vane  would  soon  move  beyond  the  range  of  the  jet, 
it  would  be  necessary,  in  order  to  obtain  continuous  action  on  a 
motor,  to  provide  a  succession  of  vanes,  which  might  be  mounted 
on  the  rim  of  a  wheel.  There  would  be,  in  consequence,  waste 
of  energy  due  to  the  motion  of  the  vanes  in  a  circle  and  to 
splattering  and  other  imperfect  action. 

If  the  velocity  of  the  jet  of  water  is  high  it  would  fail  to  spread 
fairly  over  the  plate  in  Fig.  99,  when  it  is  at  rest,  and  a  crude 
motor  of  the  sort  mentioned  would  show  a  very  poor  efficiency. 
Now  steam  has  exceedingly  high  velocity  when  discharged  from 
a  nozzle,  and  the  jet  is  more  easily  broken,  so  that  adverse  influ- 
ences have  even  a  worse  effect  than  on  water,  and  there  is  the 
greater  reason  for  following  methods  which  tend  to  avoid  waste. 
Also,  as  pointed  out  on  page  434,  the  nozzle  must  be  so  formed  as 
to  expand  the  steam  down  to  the  back  pressure,  or  expansion 
will  continue  beyond  the  nozzle  with  further  acceleration  of  the 
steam  under  unfavorable  conditions. 

It  is  easy  to  show  that  the  best  efficiency  of  the  simple  action 
of  a  jet  on  a  vane,  which  we  have  discussed,  will  be  obtained  by 
making  the  velocity  V  of  the  vane  half  the  velocity  Vt  of  the  jet. 


IMPULSE 


475 


For  if  we  differentiate  the  expression  (276)  with  regard  to  V 
and  equate  the  differential  coefficient  to  zero  we  shall  have 

F,  -  2F  -  o;        F  -  JFt; 

and  this  value  carried  into  expression  (276)  gives  for  the  work 
on  the  vane 

1™F2- 
4*     " 

but  the  kinetic  energy  of  the  jet  is 

L™Vl\ 

2   g 

so  that  the  efficiency  is  0.5. 

If  the  flat  plate  in  Fig.  99  be  replaced  by  a  semi-cylindrical 
vane  as  in  Fig.  99a,  the  direction  of  the  stream  will  be  reversed, 
and  the  impulse  will  be  twice  as  great.     If  the 
vane  as  before  has    the  velocity  V  the  relative 
velocity  of  the  jet  with  regard  to  the  vane  will 
be 

V,  -  V  FIG.  99a. 

and  neglecting  friction  this  velocity  may  be  attributed  to  the 
water  where  it  leaves  the  vane.  This  relative  velocity  at  exit 
will  be  toward  the  rear,  so  that  the  absolute  velocity  will  be 

V  -  (Vl  -  F)  =  2V  -  Vr 
The  change  of  velocity  or  negative  acceleration  will  be 

V,  -  (2V  -  F,)  -  2  (F,  -  F), 
and  the  impulse  is  consequently 


,  -F). 


The  work  of  the  impulse  becomes 


-  .2  (V,  -  V)  V  =  2   -  (V,V  -  F2)     .     .   (277) 

o  o 

The  maximum  occurs  when 

-±.  (VlV  -  F2)  ..  F,  -  2  F'=  o    or    F  -  J  F,. 


476  STEAM-TURBINES 

But  this  value  introduced  in  equation  (277)  now  gives 


which  is  equal  to  the  kinetic  energy  of  the  jet,  and  consequently 
the  efficiency  without  allowing  for  losses  appears  to  be  unity. 

Certain  water-wheels  which  work  on  essentially  this  principle 
give  an  efficiency  of  0.85  to  0.90.  The  method  in  its  simplest 
form  is  not  well  adapted  to  steam  turbines,  but  this  discussion 
leads  naturally  to  the  treatment  of  all  impulse  turbines  now 
made. 

Reaction.  —  If  a  stream  of  water  flows  through  a  conical 
nozzle  into  the  air  with  a  velocity  Vl  as  in  Fig.  100,  a  force 

R  =  f  v,  .......  (278) 

o 

will  be  exerted  tending  to  move  the  vessel 
from  which  the  flow  takes  place,  in  the 
contrary  direction.  Here  again  w  is  the 
weight  discharged  per  second,  and  g  is  the 
acceleration  due  to  gravity.  The  force  R 
FIG.  ioo.  is  called  the  reaction,  a  name  that  is  so 

commonly  used  that  it  must  be  accepted. 

Since  the  fluid  in  the  chamber  is  at  rest,  the  velocity  V1  is  that 
imparted  by  the  pressure  in  one  second,  and  is  therefore  an 
acceleration,  and  the  force  is  therefore  measured  by  the  product 
of  the  mass  and  the  acceleration.  However  elementary  this  may 
appear,  it  should  be  carefully  borne  in  mind,  to  avoid  future 
confusion. 

If  steam  is  discharged  from  a  proper  expanding  nozzle,  which 
reduces  the  pressure  to  that  of  the  atmosphere,  its  reaction  will 
be  very  nearly  represented  by  equation  (278),  but  if  the  expansion 
is  incomplete  in  the  nozzle  it  will  continue  beyond,  and  the 
added  acceleration  will  affect  the  reaction.  On  the  other  hand, 
if  the  expansion  is  excessive  there  will  be  sound  waves  in  the 
nozzle  and  other  disturbances. 


GENERAL  CASE  OF  IMPULSE 


477 


The  velocity  of  the  jet  depends  on  the  pressure  in  the  chamber, 
and  if  it  can  be  maintained,  the  velocity  will  be  the  same  rela- 
tively to  the  chamber  when  the  latter  is  supposed  to  move.  The 
work  will  in  such  case  be  equal  to  the  product  of  the  reaction, 
computed  by  equation  (278),  and  the  velocity  of  the  chamber. 
There  is  no  simple  way  of  supplying  fluid  to  a  chamber  which 
moves  in  a  straight  line,  and  a  reaction  wheel  supplied  with 
fluid  at  the  centre  and  discharging  through  nozzles  at  the  cir- 
cumference is  affected  by  centrifugal  force.  Consequently, 
as  there  is  now  no  example  of  a  pure  reaction  steam  turbine,  it 
is  not  profitable  to  go  further  in  this  matter.  It  is,  however, 
important  to  remember  that  velocity,  or  increase  of  velocity,  is 
due  to  pressure  in  the  chamber  or  space  under  consideration, 
and  is  relative  to  that  chamber  or  space. 

General  Case  of  Impulse.  —  In  Fig.  101  let  ac  represent  the 
velocity  Vl  of  a  jet  of  fluid,  and  let  V  represent  the  velocity  of  a 
curved  vane  ce.     Then  the 
velocity  of  the  jet,  relative       —  b 

to  the  vane  is  V2  equal 
to  be.  This  has  been  drawn 
in  the  figure  coincident 
with  the  tangent  at  the  end 
of  the  vane,  and  in  general 
this  arrangement  is  desir- 
able because  it  avoids 
splattering. 

If  it  be  supposed  that 
the  vane  is  bounded  at 
the  sides  so  that  the  steam 
cannot  spread  laterally  and 

if  friction  can  be  neglected,  the  relative  velocity  F3  may  be 
assumed  to  equal  F2.  Its  direction  is  along  the  tangent  at 
the  end  e  of  the  vane.  The  absolute  velocity  F4  can  be  found 
by  drawing  the  parallelogram  efgh  with  ef  equal  to  F,  the 
velocity  of  the  vane. 

The  absolute  entrance  velocity  Vl  can  be  resolved  into  the 


FIG. 


4/8  STEAM-TURBINES 

two  components  ai  and  ic,  at  right  angles  to  and  along  the  direc- 
tion of  motion  of  the  vane.  The  former  may  be  called  the 
velocity  of  flow,  F/?  and  the  latter  the  velocity  of  whirl,  Vw. 
In  like  manner  the  absolute  exit  velocity  may  be  resolved  into 
the  components  ek  and  kg,  which  may  be  called  the  exit  velocity 
of  whirl  F/,  and  the  exit  velocity  of  flow,  F/. 

The  kinetic  energy  corresponding  to  the  absolute  exit  velocity 
F4  is  the  lost  or  rejected  energy  of  the  combination  of  jet  and 
vane,  and  for  good  efficiency  should  be  made  small.  The  exit 
velocity  of  whirl  in  general  serves  no  good  purpose  and  should 
be  made  zero  to  obtain  the  best  results. 

The  change  in  the  velocity  of  whirl  is  the  retardation  or  nega- 
tive acceleration  that  determines  the  driving  force  or  impulse; 
and  the  change  in  the  velocity  of  flow  in  like  manner  produces 
an  impulse  at  right  angles  to  the  motion  of  the  vane,  which  in 
a  turbine  is  felt  as  a  thrust  on  the  shaft. 

Let  the  angle  acd  which  the  jet  makes  with  the  line  of  motion 
of  the  vane  be  represented  by  a,  and  let  /?  and  7  represent  the 
angles  bed  and  leh  which  the  tangents  at  the  entrance  and  exit  of 
the  vane  make  with  the  same  line. 

The  driving  impulse  is  in  general  equal  to 

P  =  j  (F.  -  F.')  ; (279) 

and  the  thrust  is  equal  to 

r-j(F,-F/) (280) 

which  may  be  written 

T  =  -  (Vl  sin  a  -  F3  sin  7)    ...   (281) 

o 

If  there  is  no  velocity  of  whirl  at  the  exit  the  impulse  becomes 

'-?'•— <*> 

The  work  delivered  to  the  vane  per  second  is 

"7f> 

W=-VVlcosa, (283) 

o 


GENERAL  CASE  OF  IMPULSE 


479 


and  since  the  kinetic  energy  of  the  jet  is  WV*  -*•  2g  the  effi- 
ciency is 

(284) 


e  =  2  -—  -  cos  a 
* 


To  find  the  relations  of  the  angles  a,  /?,  and  7,  we  have  from 
inspection  of  Fig.  102  in  which  el  is  equal  to  ef, 

Vl  sin  a  =  F2  sin  /?  ......  (285) 

V  =  F2  cos  7  ........  (286) 

V  =  V1  cos  a  —  V2  cos  /?; 


from  which 


and 


sn  a 


sn  a  cos  7 
-  .     , 
sin  ? 


^in  /? 
sin  f)  cos  a  —  cos  /?  sin  a  =  sin  a  cos  7 


sin  (/?  —  a)  =  sin  a  cos  7      .......   (287) 

The  equations  given  above  may 
be  applied  to  the  computation 
of  forces,  work,  and  efficiency 
when  w  pounds  of  fluid  are  dis- 
charged from  one  or  several  noz- 
zles and  act  on  one  or  a  number 
of  vanes;  that  is,  they  are  directly 
applicable  to  any  simple  impulse 
turbine. 

Example.  Let  Vv  the  velocity 
of  discharge,  be  3500  feet  per 
second  as  computed  for  a  nozzle 
on  page  444,  and  let  a  =  7  =  30°. 


By  equation  (287) 
sin  (/?  —  «)  =  sin  a  cos  7  =  0.5  X  0.866  =  0.433, 
.'.     p  -  a  =  25    40';  p  =  55°  40' 

,,       ,,  sin  a  0.5 

^T 
0.826 


2120 


2         i 

1  sin  (3 

F=  F2  cos  7=  2120  X  0.826=  1835 
e  =  2  X  1835  X  0.826  -v-  3500  =  0.909. 


48o 


STEAM-TURBINES 


No  Axial  Thrust.  —  The  builders  of   impulse  steam-turbines 

attribute  much  importance  to 
avoiding  axial  thrust,  which  can 
be  done  by  making  the  entrance 
and  exit  angles  of  the  vanes 
equal,  provided  that  friction 
and  other  resistances  can  be 
neglected.  This  is  evident  from 
equation  (280),  provided  that 
f  7  is  made  equal  to  f)  and  F2 
equal  to  F3,  and  also  that  Vl 
sin  a  is  replaced  by  F2  sin  /?. 
Or  the  same  conclusion  can  be 
drawn  from  Fig.  103  because 
in  this  case 


FIG.  103. 


ai  =  Vl  sin  a  —  F2  sin  /?  =  F2  sin  7  =  hi, 

and  consequently  there  is  no  axial  retardation. 

The  de  Laval  turbine  has  only  one  set  of  nozzles  which  expand 
the  steam  at  once  to  the  back  pressure,  and  consequently  the 
velocity  of  the  vanes  is  very  high  and  even  with  small  wheels 
it  is  difficult  to  balance  them  satisfactorily.  This  difficulty  is 
met  by  the  use  of  a  flexible  shaft,  and  consequently  axial  thrust 
is  likely  to  be  troublesome;  as  a  matter  of  fact  the  turbine  is  so 
arranged  that  the  axial  force  (if  there  is  any)  shall  be  a  pull. 
The  importance  of  avoiding  axial  thrust  in  other  types  of  impulse 
turbines  does  not  appear  to  be  so  great,  and  in  some  cases  axial 
thrust  may  be  an  advantage,  for  example  in  marine  propulsion. 

If  7  is  made  equal  to  /?  in  equation  (287)  we  have 

sin  ft  cos  a.  —  cos  /?  sin  a  =  sin  a  cos  /? 


cot  /?  =  J  cot  a 


(288) 


and  from  inspection  of  Fig.  103  it  is  evident  that  V  is  half  of  the 
velocity  of  whirl  or 

(289) 


DESIGN    OF   A    SIMPLE    IMPULSE-TURBINE  481 

If  this  value  is  carried  into  equations  (283)  and  (284)  the 
work  and  efficiency  become 

W  =  %   -    V*cos*ct (290) 

o 

and 

e  =  cos2  a (29J) 

This  freedom  from  axial  thrust  appears  to  be  purchased 
dearly  unless  the  accompanying  reduction  of  velocity  of  the 
wheel  is  to  be  considered  also  of  importance. 

Example.  If  as  in  the  preceding  case  the  velocity  of  discharge 
is  3500  feet  per  second,  and  if  a  is  30°,  we  have  now  the  following 
results, 

cot/9  =  |  cot  a  =  £  X  1.732  =  0.866  /.  /?  =  49°  10' 
V  =  \  V1  cos  a  =  J  X  3500  X  0.866  =  1515 
e  =  cos2  30°  =  0.75. 

Effect  of  Friction.  —  The  direct  effect  of  friction  is  to  reduce 
the  exit  velocity  from  the  vane;  resistance  due  to  striking  the 
edges  of  the  vanes,  splattering,  and  other  irregularities,  will 
reduce  the  velocity  both  at  entering  and  leaving.  The  effect  of 
friction  and  other  resistances  is  two-fold;  the  effect  is  to  reduce 
the  efficiency  of  the  wheel  by  changing  kinetic  energy  into  heat, 
and  to  reduce  the  velocity  at  which  the  best  efficiency  will  be 
obtained.  There  does  not  appear  to  be  sufficient  data  to  permit 
of  a  quantitative  treatment  of  this  subject.  Small  reductions 
from  the  speed  of  maximum  efficiency  will  have  but  small  effect. 

The  question  as  to  what  change  shall  be  made  in  the  exit 
angle  (if  any)  on  account  of  friction  will  depend  on  the  relative 
importance  attached  to  avoiding  velocity  of  whirl  and  axial 
thrust.  If  the  latter  is  considered  to  be  the  more  important, 
then  7  should  be  made  somewhat  larger  so  that  the  exit  velocity 
of  flow  may  be  equal  to  the  entrance  velocity  of  flow.  But  if  it 
is  desired  to  make  the  exit  velocity  of  whirl  zero,  then  y  should  be 
somewhat  decreased. 

Design  of  a  Simple  Impulse  Turbine.  —  The  following  compu- 
tation may  be  taken  to  illustrate  the  method  of  applying  the 


482  STEAM-TURBINES 

foregoing  discussion  to  a  simple  impulse  turbine  of  the  de  Laval 
type. 

Assume  the  steam-  pressure  on  the  nozzles  to  be  150  pounds 
gauge  and  that  there  is  a  vacuum  of  26  inches  of  mercury;  required 
the  principal  dimension  of  a  turbine  to  deliver  150  brake  horse- 
power. 

The  computation  on  page  444  for  a  steam-nozzle  under  these 
conditions  gave  for  the  velocity  of  the  jet,  allowing  0.15  for 
friction,  Vl  =  3500  feet  per  second.  The  throat  pressure  was 
taken  to  be  96  pounds  absolute,  giving  a  velocity  at  the  throat 
of  1480  feet  per  second.  The  dryness  factor  was  0.967  at  the 
throat;  at  the  exit  this  factor  was  0.835  for  0.15  friction  and  for 
adiabatic  expansion  was  0.795. 

The  thermal  efficiency  for  adiabatic  expansion  with  no  allow- 
ance for  friction  or  losses  whatsoever,  as  for  an  ideal  non-con- 

ducting engine,  is  given  by  equation  (144),  page  136,  as 

• 

x/s  811.8 

e  =  i  --  3-3  -  =i  --  =  0.262 


ri  +  &  ~  &  856.8  +  337.9  -  94.2 

the  corresponding  heat  consumption  is 

42.42  -f-  0.262  =  162, 

by  the  method  on  page  144. 

Let  the  angle  of  the  nozzle  be  taken  as  30°  as  on  page  481, 
then  the  angle  J3  becomes  49°  10',  the  efficiency  is  0.75  and  the 
velocity  of  the  vanes  must  be  1515  feet  per  second. 

Suppose  that  ten  per  cent  be  allowed  for  friction  and  resistance 
in  the  vanes,  and  that  the  friction  of  the  bearings  and  gears  is 
ten  per  cent;  then,  remembering  that  0.15  was  allowed  for  the 
friction  in  the  nozzle,  and  that  the  efficiency  deduced  from  the 
velocities  is  0.75,  the  combined  efficiency  of  the  turbine  should 
be 

0.262  X  0.75  X  0.85  X  0.9  X  0.9  =  0.135; 

which  corresponds  to 

42.42  -f-  0.135  =  3*4  B.T.U. 
per  horse-power  per  minute. 


DESIGN    OF   A   SIMPLE    IMPULSE    TURBINE 


483 


Now  it  costs  to  make  one  pound  of  steam  at  150  pounds  by 
the  gauge  or  165  pounds  absolute,  from  feed  water  at  126°  F. 
(2  pounds  absolute) 

ri  +  Vi  ~  &=  856-8  +  337-9  ~  94-2  =  noi  B.T.U., 
consequently  314  B.T.U.  per  horse-power  per  minute  correspond 
to 

314   X   60   -r-    IIOI  =  I7.I 

pounds  of  steam  per  horse-power  per  hour. 
The  total  steam  per  hour  for  150  horse-power  appears  to  be 

150  X  17.1  =  2570. 

If  the  nozzle  designed  on  page  444  be  taken  it  appears  that 
five  would  not  be  sufficient,  as 
each  would  deliver  only  500 
pounds  of  steam  per  hour.  But 
if  allowance  be  made  for  a  mod- 
erate  overload,  six  could  be 
supplied. 

Not  uncommonly  turbines  of 
this  type  are  run  under  speed  as 
a  matter  of  convenience.  Sup- 
pose, for  example,  the  speed  of 
the  vanes  is  only  0.35  of  the 
velocity  of  whirl,  instead  of 
0.5;  that  is,  in  this  case  take 
V  =  1050. 

This  case  is  represented  by  Fig.  104,  from  which  it  is  evident 
that 

V/  =  V/  =  ai  =  Vl  sin  30°  =  3500  X  0.5  =  1750 

Vw=  Vl  cos  30°  =  3500  X  0.866=3030 
tan  /5  =  ai  -f-  id  =  1750^-  (3030  —  1050)  =  0.884 

/?  =  41°  3°'- 

The  two  triangles  aid  and  elk  are  equal,  and 
le  =  id  =  3030  -  1050  =  1980; 


FIG.  104. 


484  STEAM-TURBINES 

consequently  the  exit  velocity  of  whirl  is 

W/  =  ek  =  1050  —  1980  =  —  930. 
Consequently  the  work  delivered  to  the  vane  is 

PV  =  -  [3030  -  (-  930)]  1050=  -  3960  X  1050 
g  S 

w 
=  416000  —  • 

g 

But  the  kinetic  energy  is  wV^  -*-  2g,  so  that  the  efficiency  is 

416000  X  2  -f-  3500    =  0.68. 
The  combined  efficiency  of  the  turbine  therefore  becomes 

0.262  X  0.68  X  0.85  X  0.9  X  0.9  =  0.123 
instead  of  0.135;  and  the  heat  consumption  becomes 
42.42  -*-  0.123  =  345  B.T.U. 

per  horse-power  per  minute;  and  the  steam  consumption  increases 
to 

345  X  60  -r-  1099  =  18.8 

pounds  per  horse- power  per  hour.     The  total  steam  per  hour 
appears  now  to  be  about 

18.8  X  150  =  2820, 

so  that  six  nozzles  like  that  computed  on  page  444  would  give 
only  a  margin  for  governing. 

If  the  turbine  be  given  twelve  thousand  revolutions  per  minute 
the  diameter  at  the  middle  of  the  length  of  the  vanes  will  be 

D  =  1050  X  12  X  60  -r-  (3.14  X  12000)  =  20  inches. 

The  computation  on  page  444  gave  for  the  exit  diameter  of 
the  nozzle  1.026  inches,  and  as  the  angle  of  inclination  to  the 
plane  of  the  wheel  is  30°,  the  width  of  the  jet  at  that  plane 
would  be  twice  the  exit  diameter  or  somewhat  more,  due  to  the 
natural  spreading  of  the  jet.  The  radial  length  of  the  vanes 
may  be  made  somewhat  greater  than  an  inch,  perhaps  iiV  inches. 
The  circumferential  space  occupied  by  the  six  jets  will  be  about 


TESTS    ON   A    DE    LAVAL   TURBINE 


485 


12  J  inches  out  of  62.8  inches  (the  perimeter),  or  somewhat  less 
than    one-fifth.       The    section    of    the    nozzle    is    shown    by 


FIG.  106. 


FIG.  105. 

Fig.  105,  and  the  form  of  the  vanes  may  be  like  Fig.  106. 
In  this  case  the  thickness  of  a  vane  is  made  half  the  space 
from  one  vane  to  the  next,  or  one-third  the 
pitch  from  vane  to  vane.  The  normal  width 
of  the  passage  is  made  constant,  the  face  of  one 
vane  and  the  back  of  the  next  vane  being  struck 
from  the  same  centre.  The  form  and  spacing 
of  vanes  can  be  determined  by  experience  only 
and  appears  to  depend  largely  on  the  judgment 
of  the  designer.  In  deciding  on  the  axial  width 
of  the  vanes  it  must  be  borne  in  mind  that 
increasing  that  width  increases  the  length  and  therefore  the 
friction  of  the  passage;  but  that  on  the  other  hand,  decreasing 
the  width  increases  the  curvature  of  the  passage  which  may  be 
equally  unfavorable.  Sharply  curved  passages  also  tend  to 
produce  centrifugal  action,  by  which  is  meant  now  a  tendency  to 
crowd  the  fluid  toward  the  concave  side  which  tends  to  raise 
the  pressure  there,  and  decreases  it  at  the  convex  side.  Mr. 
Alexander  Jude,*  for  a  particular  case  with  a  steam  velocity  of 
1000  feet  per  second,  computes  a  change  of  pressure  from  100  to 
107.1  pounds  on  the  concave  side  and  a  fall  to  93.4  on  the  convex 
side.  Even  if  this  case  should  appear  to  be  extreme  there  is  no 
question  that  sharp  curves  are  to  be  avoided  in  designing  the 
steam  passages. 

Tests  on  a  de  Laval  Turbine.  —  The  following  are  results  of 
tests  on  a  de  Laval  turbine  made  by  Messrs.  J.  A.  McKenna 


*   Theory  of  the  Steam  Turbine,  p.  49. 


486 


STEAM-TURBINES 


and  J.  W.  Regan  *  and  by  Messrs.  W.  W.  Ammen  and  H.  A.  C. 
Small.f 


Regan  and  McKenna. 

Ammen  and  Small. 

Number  of  nozzles 

6 

153 
140 

24-3 
19.7 

355 
0.903 

6 
154 
131-4 
25.2 

18.0 

326 
1016 

3740 
0.271 
0.900 

6 

154.7 
in  .9 

25-i 
20.9 

379 

0.864 

6 

148.8 
136.9 
26 

19-3 

35° 
1056 

3470 
°-3°5 
0.914 

6 
148.8 
78.8 
26 

23.2 

426 
1037 

377° 
0.275 
0.885 

3 
i5°-7 
140.4 
26.4 

21-5 
374 

0.880 

Boiler  pressure  gauge      .    .    . 
Steam  chest  pressure  .... 
Vacuum,  inches    

Steam  per  brake,  horse-power 
per  hour    .    . 

B.T.U.  per  brake  horse-power 
per  minute 

Velocity  of  vanes      

Velocity  of  jet 

Ratio  of  velocities 

Efficiency  of  electric  generator 

Compound  Steam-Turbines.  —  There  are  three  ways  in  which 
impulse-turbines  have  been  compounded  (i)  the  steam  may  be 
expanded  at  once  to  the  back-pressure  and  then  allowed  to  act 
on  a  succession  of  moving  and  stationary  vanes,  (2)  the  steam 
may  flow  through  a  succession  of  chambers  each  of  which  has 
in  it  one  simple  impulse- wheel  or  (3)  a  combination  of  these 
methods  may  be  made,  the  steam  flowing  through  a  succession 
of  chambers  in  each  of  which  it  acts  on  a  succession  of  moving 
and  stationary  vanes.  The  first  method  which  gives  a  very 
compact  but  an  inefficient- wheel,  is  used  for  the  backing-turbine 
of  the  Curtis  marine- turbine.  The  second  method  is  used  in  the 
Rateau  turbine,  which  has  usually  a  large  number  of  chambers. 
The  third  method  is  found  in  the  Curtis  turbine  which  has  from 
two  to  seven  chambers  in  each  of  which  are  from  two  to  four  sets 
of  revolving  vanes. 

The  Parsons  turbine,  which  is  an  impulse-reaction  wheel,  has 
a  very  large  number  of  sets  of  moving  vanes,  i.e.,  from  fifty  to 
one  hundred  and  fifty. 

The  various  forms  of  compound  turbines  have  been  devised 
to  reduce  the  speed  of  the  vanes  and  the  revolutions  per  minute 
to  convenient  conditions  without  sacrificing  the  efficiency. 

*  Thesis,  M.I.T.  1903.  f  Thesis,  M.I.T.  1905. 


VELOCITY   COMPOUNDING 


487 


Velocity  Compounding.  —  In  Fig.  107,  let  Vl  represent  the 
velocity  of  a  jet  of  steam  that  is  expanded  in  a  proper  nozzle 
down  to  the  back- pressure. 
Suppose  it  acts  on  an  equal- 
angled  (/?  =  7)  vane  which  has 
the  velocity  V.  The  relative 
velocity  at  entrance  to  that 
vane  is  V2  and  this  velocity 
reversed  and  drawn  at  F3  may 
represent  the  exit  velocity, 
neglecting  friction.  ¥4  is  the 
absolute  velocity  at  exit  from 
the  vane,  which  may  be  re- 
versed by  an  equal-angled 
stationary  guide,  and  then 
becomes  the  absolute  velocity 
F/  acting  on  the  next  vane. 
The  diagram  of  velocities  for 
the  second  moving  vane  is 
composed  of  the  lines  lettered 
F/,  F2',  F3'  and  F/;  the 
last  of  these  is  reversed  by  a 
stationary  guide,  and  the 
velocities  of  the  third  vane  are 
FI",  F/',  F3"  and  F4".  The 
diagram  is  constructed  by 
dividing  the  velocity  of  whirl 

Vw  =  V1  cos  a 

into  six  equal  parts,  and  the  final  exit  velocity  F4"  is  vertical, 
indicating  that  there  is  no  velocity  of  whirl  at  that  place. 

It  is  immediately  evident,  since  the  velocity  of  flow  is  unaltered 
in  Fig.  107,  and  since  there  is  no  exit  velocity  of  whirl  that  the 
efficiency  neglecting  friction  is  the  same  as  for  Fig.  103,  namely 

e  =  cos2  a 


as  given  by  equation  (291)  page  481. 


488 


STEAM-TURBINES 


It  is,  however,  interesting  to  determine  the  work  done  on  each 
vane;  the  sum  of  the  works  of  course  leads  to  the  same  result. 
In  Fig.  107  the  velocity  of  whirl  at  entrance  to  the  first  vane  is 

Vl  cos  a 
and  the  velocity  of  whirl  at  exit  is 

—  F4cosa1  =  --  -  FjCosa; 
consequently  the  work  done  on  the  vane  is 

-    Fj  cos  a  -  (  —  *-  Vl  cos  aj  -F1  cos  a, 

because  F  was  made  equal  to  one-sixth  of  the  velocity  of  whirl. 
This  expression  reduces  to 

10  w  Tr ,       , 
—  -  F2cos2a. 

36  g 
The  second  and  third  vanes  receive  the  works 

6  iv  ,r 2       2  .     2  w      2       , 

—  -  F,2  cos2  a  and  —  -  F2  cos2  a 
36  £  3°  g 

so  that  the  resultant  work  is 

1  -  Ft2  cos2  a 

o 

and  the  efficiency  is  evidently  given  by  the  expression  already 
quoted.  The  most  instructive  feature  of  this  discussion  is  that 
the  relation  of  the  works  done  on  the  three  vanes  is 

5>  3»  i- 

A  similar  investigation  will  show  that  the  distribution  among 
four  vanes  is 

7>  5>  3>  i- 

The  first  figure  in  such  a  series  is  obtained  by  adding  to  the 
number  of  vanes  one  less  than  that  number;  and  each  succeeding 
term  is  two  units  smaller.  Thus  seven  vanes  give  the  distribu- 
tion 

i3»         JI>          9»  7>  5>  3i         I- 


VELOCITY    COMPOUNDING  489 

It  is  considered  that  this  type  of  turbine  cannot  be  made  to 
give  good  efficiency  in  practice  on  account  of  large  losses  in  passing 
through  a  succession  of  vanes  and  guides,  especially  as  the  steam 
in  the  earlier  stages  has  high  velocities.  The  turbine,  however, 
has  certain  advantages  when  used  as  a  backing  device  for  a 
marine-turbine,  in  that  it  may  be  very  compact,  and  can  be  placed 
in  the  low-pressure  or  exhaust  chamber,  so  that  it  will  experience 
but  little  resistance  when  running  idle  during  the  normal  forward 
motion  of  the  ship. 

In  dealing  with  this  problem  it  is  convenient  to  transfer  the 
construction  to  the  combined  diagram  at  abi,  Fig.  107 ;  diagrams 
for  guides  like  that  made  up  of  the  velocities  F3,  V±  and  V±  being 
inverted  for  that  purpose.  It  is  clear  that  the  absolute  velocities 
at  exit  from  the  nozzle  and  the  guides  are  represented  by  F^F/ 
and  F/',  while  the  relative  velocities  are  F2,  F2'  and  F2"  which 
with  no  axial  thrust  are  equal  to  F3,  F3'  and  F3".  The  absolute 
velocity  at  entrance  to  a  given  guide  is  taken  as  equal  to  the  abso- 
lute velocity  at  exit  from  the  preceding  vane,  thus  F/  is  equal 
to  F4,  etc.  The  last  absolute  velocity  F /'  is  equal  to  ai  the 
constant  velocity  of  flow. 

The  angles  a,  /?,  av  /?x,  a2  and  /?2  are  properly  indicated  as  may 
be  seen  by  comparing  the  original  with  the  combined  diagram. 

If  the  diagram  is  accurately  drawn  to  a  large  scale,  the  velocities 
and  angles  can  be  measured  from  it,  or  they  may  readily  be 
calculated  trigonometrically.  Thus 

Q         sin  a  sin  a 

tan  B  = ;  tana,  =- etc., 

I  cos  a  f  cos  a 

F2  =  Fj  sin  a  cosec  /?;     F/  =  Fx  sin  a  cosec  av  etc. 

The  radial  length  of  the  vanes  and  guides  must  be  increased 
inversely  proportional  to  the  velocities,  using  relative  velocities 
for  the  vanes  and  absolute  velocities  for  the  guides. 

There  appears  to  be  no  reason  why  the  guides  should  be 
relieved  from  axial  thrust  provided  they  can  be  properly  sup- 
ported. 


49° 


STEAM-TURBINES 


FIG.  108. 


Except  that  the  passages  in  the  guides  might  become  too 
long  or  too  sharply  curved,  they  might  all  be  given  the  same 
delivery  angle  as  the  nozzle,  and  thus  a  notable  improvement 

in    economy    could    be 
realized.     In    Fig.    108 
the    velocities    Vv    V2 
and  V±,  are  drawn  in 
the   usual   manner,    V3 
being  equal  to  F2;  the 
velocity    V \  is  laid  off 
along  the  same  line  as 
Vl  and  is  lettered   F/ 
and  serves  as  the  initial 
velocity  for  a  new  con- 
struction as   indicated.     F4'  is  in  like  manner  laid  off  for  F/', 
and  thus  the  diagram  is  completed.     The  velocity  of  the  vanes 
of  course  remains  constant  with  the  value  F. 

Following  the  problem  on  page  444  for  a  nozzle  discharging 
from  150  pounds  by  the  gauge  into  26  inches  of  vacuum  we  have 
Fj  =  3500  feet  per  second  with  y  =  0.15.  The  value  of  F  may 
be  taken  as  620  feet  per  second,  which  gives  a  diagram  with  no 
final  velocity  of  whirl. 

The  exit  velocity  of  whirl  from  the  first  set  of  vanes  is  —  1830 
feet  per  second  as  measured  on  the  diagram,  and  since  the  initial 
velocity  of  whirl  is 

Vl  cos  a  =  3500  X  0.866  =  3030 
the   retardation   is 

3030  -  (  -  1830)  =  4860. 
The  retardation  for  the  second  set  of  vanes  is 

2160  —  (  —  880)  =  3040, 
and  for  the  third  set  is  1320,  so  that  the  work  of  the  impulse  is 

(4860  +  3040  +  1320)   X  620  -  =  5720000-, 

o  o 


EFFECT   OF   FRICTION  491 

and  as  the  intrinsic  energy  of  the  jet  is 

w  T  ,  ,       ,  -  2  w  w 

_KI   -  j  MOO  j.  -  6I.JOOOJ 

the  efficiency  of  this  arrangement  without  losses  and  friction 

appears   to   be 

5720  -T-  6125  =  0.92. 

Effect  of  Friction.  —  The  effect  of  friction  is  to  change  some 
of  the  kinetic  energy  into  heat,  thereby  reducing  the  velocity  and 
at  the  same  time  drying  the  steam  and  increasing  the  specific 
volume  so  that  the  length  of  the  guides  and  vanes  must  be 
increased  at  a  somewhat  larger  ratio  than  would  otherwise  be 
required. 

A  method  of  allowing  for  friction  is  to  redraw  the  diagram  of 
Fig.  107,  shortening  the  lines  that  represent  the  velocities  to 
allow  for  friction. 

In  order  to  bring  out  the  method  clearly  an  excessive  value 
will  be  assigned  to  the  coefficient  for  friction,  namely,  y  =  0.19, 
so  that  the  equation  for  velocity  may  have  for  its  typical  form 


F0  =  \/2gh  (i  —  y)  =  0.9 

Again  the  coefficient  will  be  assumed  to  be  constant  for  sake  of 
simplicity,  more  especially  as  but  little  is  known  with  regard  to 
its  real  value. 

The  diagram  shown 
by  Fig.  109  was  drawn 
by  trial  with  Vl  =  3500 
and  with  a  =  30°.  It 
appeared  necessary  to 
reduce  V  to  380  feet 
per  second,  instead  of 
505  feet,  which  would 
be  proper  without  fric- 
tion, this  latter  quantity 

being  one-sixth  of  the  FIG.  109. 

initial  velocity  of  whirl, 

Vw  =  Vl  cos  a  =  3500  X  0.866  =  3030. 


49  2  STEAM-TURBINES 

Starting  with  Vl  the  velocity  of  the  jet,  the  triangle  Vv  V,  F, 
is  drawn  to  determine  the  initial  relative  velocity  for  the  first  set 
of  vanes.  The  exit  velocity  F3  is  made  equal  to  0.9  F2,  and  the 
triangle  F3,  F,  V \  is  drawn  to  determine  the  absolute  velocity 
at  exit  ¥4  from  the  guides.  This  is  taken  to  be  the  velocity  at 
entrance  to  the  guides,  but  the  exit  velocity  from  them  is  taken  to 
be  F/  =  0.9  ¥4.  Two  repetitions  of  this  process  complete  the 
diagram.  The  velocities  of  whirl  at  entrance  to  the  three  sets  of 
vanes  as  measured  on  the  diagram  are 

3030  1780  800, 

and  the  velocities  of  whirl  at  exit  from  those  vanes  are 

-  1890  -  880  -  o, 

so  that  the  negative  accelerations  are 

4920  2660  800, 

making  a  total  of  8380.     Since  the  velocity  of  the  vanes  is  380 
feet  per  second  the  work  delivered  to  the  turbine  is 

8380  X  380  -  =  3180000  — , 
g  S 

and  consequently,  using  the  kinetic  energy  already  computed  for 
the  jet  on  the  preceding  page,  the  efficiency  is 

3180000  -r-  6125000  =  0.52. 

This  method  preserves  the  equality  of  the  angles  of  the  vanes 
and  guides,  but  does  not  avoid  axial  thrust,  for  Fig.  109  shows  a 
large  reduction  of  the  velocity  of  flow,  and  as  there  are  no  reversals 
of  flow,  the  reduction  is  a  measure  of  the  impulse  producing 
axial  thrust.  Nearly  half  of  the  thrust  is  borne  by  the  fixed 
guides,  and  it  is  to  be  borne  in  mind  that  the  assumption  of  an 
exaggerated  coefficient  for  friction  greatly  exaggerates  this 
feature,  which  in  practice  may  not  be  very  troublesome. 

To  entirely  avoid  axial  thrust  it  appears  to  be  necessary  only 
to  slightly  increase  the  angle  y  at  the  exit  from  the  vane;  the 
angles  of  the  guides  may  be  reduced  if  desired  as  an  offset. 


PRESSURE   COMPOUNDING 


493 


FIG.  no. 


In  Fig.  no  an  attempt  is  made  to  avoid  axial  thrust  on 
the  vanes,  and  at  the  same  time  to  retain  a  fair  efficiency 
by  making  the 
delivery  angle  of 
the  guides  constant. 

A  calculation  like 
that  on  page  492 
indicates  that  an 
efficiency  of  0.76 
might  be  expected 
in  this  case.  It  is 
quite  likely  that 
in  practice  there 
might  be  difficulty 

in  making  the  delivery  angle  of  the  guide  as  small  as  30°, 
but  it  appears  as  though  the  common  idea  that  it  is  practically 
impossible  to  make  an  economical  turbine  on  this  principle  is 
not  entirely  justified. 

Pressure  Compounding.  —  The  second  method  of  compounding 
impulse  turbines  with  a  number  of  chambers  each  containing 
a  single  impulse  wheel  like  that  of  the  de  Laval  turbine  requires 
a  large  number  of  stages  to  give  satisfactory  results.  For  sake 
of  comparison  with  preceding  calculation  we  will  take  the 
same  initial  and  final  pressure  and  the  same  angle  for  the  nozzles, 
namely,  150  pounds  by  the  gauge  and  26  inches  vacuum,  and 
a  =  30°. 

Nine  stages  in  this  case  will  give  approximately  the  same 
speed  of  the  vanes  as  in  the  problem  on  page  490.  The  temper- 
ature-entropy table  which  was  made  for  work  of  this  nature 
is  most  conveniently  used  with  temperature,  and  in  this  case  the 
initial  and  final  temperature  can  be  taken  as  366°  F.  and  126°  F. 
At  366°  F.  the  steam  is  found  to  be  nearly  dry  for  the  entropy 
1.56  and  that  column  will  be  taken  for  the  solution  of  this 
problem.  The  heat  contents  is  1193.3  instead  of  1194.6  as 


found    for    366°    F. 
crties   of   Steam." 


in    Table   I  of    the 
On   the   other   hand 


'Tables    of    Prop- 
the    table   gives   at 


494 


STEAM-TURBINES 


126°  for  the  heat  contents  904.9,  and  the  difference  is 
1193.3  -  904.9  =  288. 

If  we  divide  the  available  heat  into  nine  portions  we  have 
for  each 

288  -r-  9  =  32  B.T.U. 

If  again  we  take  y  =  o.i  which  may  be  excessive  in  this  case 
since,  as  will  be  evident,  simple  converging  nozzles  will  be 
required,  the  velocity  of  the  steam  jet  will  be 


Vl  =  V2  X  32.2  X  778  X  32  X  (i  -  o.i)  =  1200 

feet  per  second.     This  is  of  course  the  velocity  for  all  the  stages. 
The  choice  of  a:  =  30°  gives  for  the  velocity  of  whirl 

1200  cos  30°  =  1200  X  0.866  =  1040, 

and  the  velocity  of  the  vanes  to  give  the  maximum  economy  is 
half  of  this  or  520  feet  per  second  or  somewhat  less  if  allowance 
be  made  for  friction  and  other  losses. 

Since  we  have  to  deal  with  a  single  impulse  wheel  in  each 
chamber  and  since  the  wheels  are  usually  designed  to  avoid  axial 
thrust,  all  the  conclusions  concerning  that  type  of  wheel  may  be 
assumed  at  once  as  has  already  tacitly  been  done. 

One  of  the  important  conclusions  is  that  the  efficiency  without 
friction  as  given  by  equation  (291)  page  481  is 

e  =  cos2  «; 

with  a  =  30°,  this  gives  e  =  0.75. 

It  is  but  fair  to  say  that  a  smaller  angle  of  a  is  used  for  this 
type  of  turbine  and  that  the  range  of  temperature  is  likely  to  be 
extended  at  both  limits,  and  that  in  particular  great  importance 
is  attached  to  securing  a  good  vacuum;  28  inches  of  mercury, 
corresponding  to  one  pound  absolute,  is  commonly  obtained 
in  good  practice  with  all  compound  turbines. 

If  the  peripheral  speed  of  the  wheel  must  be  kept  down,  this 
type  of  turbine  is  likely  to  have  a  very  large  number  of  chambers. 
For  example,  if  the  speed  must  be  no  more  than  260  feet  per 
second  (half  of  520),  there  must  be  36  chambers  instead  of  9. 


PRESSURE   COMPOUNDING 


495 


This  will    give    for  the    available    heat    for    each    chamber  8 
thermal  units,  and  using  as  before  y  =  o.i  we  shall  have 


Fj  =  V2  X  32.2  X  778  X  8  X  0.9  =  600 

feet  per  second.  With  a  =  30°  the  velocity  of  whirl  is  now  520 
feet  and  the  velocity  of  the  vanes  as  stated  is  260  feet  per  second. 

The  next  question  in  the  discussion  of  this  turbine  is  the 
distribution  of  pressure.  If  the  coefficients  for  friction  and 
other  losses  are  taken  to  be  constant,  then  the  pressure  can  be 
approximately  determined  by  the  adiabatic  method. 

In  the  problem  already  discussed  32  B.T.U.  are  assigned  to 
each  stage,  and  if  this  figure  be  subtracted  nine  times  in  succes- 
sion from  the  heat  contents  1194  at  the  initial  temperature  we 
shall  have  the  values  which  may  be  used  in  determining  the 
intermediate  temperatures  from  the  temperature-entropy  table. 
Also  from  that  table  or  from  Table  I  in  the  "Tables  of 
Properties  of  Steam,"  the  corresponding  pressures  can  be 
determined.  The  work  is  arranged  in  the  following  table: 

DISTRIBUTION   OF  PRESSURE. 


Values  of  xr  -\-q- 

Temperatures. 

Pressures  absolute. 

Ratios  of  pressures. 

0 

H93 

366 

I65 

0.68 

I 

1161 

336 

112 

0.66 

2 

1129 

306 

73-2 

0.65 

3 

1097 

278 

47-6 

0.64 

4 

1065 

251 

30-4 

0.61 

5 

i°33 

224 

18.6 

0.61 

6 

1001 

199 

"•3 

0.58 

7 

969 

174 

6.56 

o-57 

8 

937 

ISO 

3-72 

o-53 

9 

90S 

126 

1.99 

o. 

The  last  column  gives  the  ratio  of  any  given  pressure  to  the 
preceding  pressure,  i.e.  112  .-165  =  0.68.  These  ratios  indicate 
that  simple  conical  converging  nozzles  will  be  sufficient  for  all 
but  the  last  stage.  With  the  usual  number  of  stages,  twenty  or 
more,  the  ratios  are  certain  to  be  larger  than  0.6  in  all  cases, 
indicating  the  use  of  converging  nozzles  throughout. 


496  STEAM-TURBINES 

To  determine  the  sizes  of  the  nozzles  or  the  passages  in  the 
guides  it  is  necessary  to  estimate  the  quality  of  the  steam  in 
order  to  find  the  specific  volume.  To  do  this  we  may  consider 
that,  of  the  heat  supplied  to  a  certain  stage  of  the  turbine,  a 
portion  is  changed  into  work  on  the  turbine  vanes,  some  part  is 
radiated,  and  the  remainder  is  in  the  steam  that  flows  from  the 
chamber  of  that  stage;  if  there  is  appreciable  leakage,  special 
account  must  be  taken  of  it,  but  both  radiation  and  leakage 
can  be  left  at  one  side  for  the  present. 

Now  in  the  case  under  consideration,  32  thermal  units  were 
assigned  to  each  stage  in  the  adiabatic  calculation  for  the 
distribution  of  pressure.  But  o.io  part  was  assigned  to  y  to 
allow  for  friction  so  that  only  0.9  was  applied  to  the  calculation 
of  velocity;  of  the  kinetic  energy  of  the  jet  0.75  only  was 
assumed  to  be  applied  to  moving  the  vanes  without  friction,  the 
remainder  being  in  the  kinetic  energy  of  the  flow  from  the 
vanes  which  was  assumed  to  be  changed  into  heat  again;  and 
further  there  was  an  allowance  of  o.i  for  losses  in  the  vanes, 
leaving  a  factor,  0.9,  to  be  applied  for  that  action.  Conse- 
quently instead  of  32  thermal  units  changed  into  work  per 
stage,  our  calculation  gives  only 

32  X  0.9  X  0.75  X  0.9  =  19.44  B.T.U. 

will  be  changed  into  work.  A  method  of  determining  the  quali- 
ties and  specific  volumes  at  the  several  nozzles  is  illustrated  in 
the  table  on  the  following  page. 

The  quantity  of  heat  changed  into  work  per  stage  is  sub- 
tracted successively,  giving  the  apparent  remaining  heat  contents 
as  set  down  in  the  tables.  At  a  given  temperature  we  may  find 
the  quality  by  subtracting  the  heat  of  the  liquid  from  the  heat 
contents  and  dividing  the  remainder  by  the  value  of  r.  The 
specific  volumes  are  determined  by  the  equation 

1)  «±  xu  +  cr, 

but  as  x  is  in  all  cases  large,  the  effect  of  &  may  be  neglected 
altogether. 


PRESSURE   COMPOUNDING 


497 


FIRST    COMPUTATION    OF   QUALITIES    AND    VOLUMES. 


Tem- 
perature 

Heat 
con- 
tents 

Heat  of 
liquid 

Value 
of 

Heat  of 
vapori- 
zation 

Quality 
(*) 

Specific  volumes 
(«c) 

w 

(xr  +  q) 

(?) 

xr 

(r) 

0 

366 

H93 

338 

855 

857 

0.998 

2-75 

2-74 

I 

336 

1174 

307 

867 

88  1 

0.984 

3-99 

3-93 

2 

306 

U54 

276 

878 

904 

0.971 

5-94 

5-77 

3 

278 

H35 

247 

888 

92S 

0.960 

8.90 

8-54 

4 

251 

IH5 

220 

895 

944 

0.948 

13-6 

12.9 

5 

224 

1096 

192 

904 

962 

0.940 

21-5 

2O.  2 

6 

199 

1076 

I67 

909 

978 

0.930 

34-3 

3J-9 

7 

174 

i°57 

142 

915 

993 

0.922 

56-9 

52.5 

8 

15° 

io37 

118 

919 

1007 

0.913 

96.9 

88.5 

9 

126 

1018 

94 

924 

IO2I 

0.905 

174 

!57-4 

By  the  aid  of  the  temperature-entropy  table,  the  qualities 
and  specific  volumes  may  be  determined  directly  with  good 
approximation,  it  being  necessary  only  to  follow  the  line  of  the 
temperature  to  an  entropy  column,  having  nearly  the  proper 
heat  contents. 

There  is  a  serious  objection  to  the  adiabatic  method,  because 
it  does  not  take  any  account  of  the  fact  that  as  the  steam  passes 
from  stage  to  stage  losing  less  heat  than  it  would  with  adiabatic 
action,  the  entropy  increases,  and  that  with  increased  entropy 
the  difference  of  heat  contents  between  two  given  temperatures 
increases.  This  will  be  very  apparent  from  inspection  of  a 
temperature-entropy  diagram  or  the  temperature-entropy  table. 
This  matter  will  be  discussed  more  at  length  in  connection  with 
the  Curtis  type  of  turbine. 

It  has  been  assumed  that  the  same  amount  of  heat  should  be 
assigned  to  each  stage  for  the  adiabatic  calculation  and  that  the 
values  of  y  to  allow  for  friction  and  losses  remain  constant. 
As  to  the  values  that  should  be  assigned  to  y,  we  have  very  little 
published  information;  it  may  be  noted  in  passing  that  our 
allowance  for  friction  in  the  nozzles  and  guides  is  probably  too 
large.  It  will  be  evident  that  there  is  no  difficulty  in  maintaining 
the  amount  assigned  to  each  stage  in  its  proper  proportion  even 


STEAM-TURBINES 


though  y  shall  be  varied  from  stage  to  stage.  For  example,  our 
choice  of  o.i  for  both  y  and  yl  gives 

32  X  0.9  X  0.9  =  25.92  B.T.U., 

which  multiplied  by  0.75,  the  efficiency  due  to  the  angles  and 
velocities,  gives  19.44  B.T.U.  as  above.  Let  it  be  assumed  for 
the  moment  that  the  above  product  shall  be  kept  constant,  so  as 
to  obtain  the  same  velocity  of  jet  in  each  stage.  Then  the 
following  table  exhibits  a  way  of  accomplishing  this  purpose 
while  varying  y  and  y^: 


Stage 

i 

2 

3 

4 

5 

6 

7 

8 

9 

V 

o  08 

o  o8< 

O   OQ 

O   OCK 

O.  IO 

O.  IOC 

O.  II 

O.  II< 

O.  12 

yl    

0.088 

0.091 

0.094 

0.097 

0.  10 

0.103 

0.106 

0.109 

0.  112 

(x-y)d-yi) 

0.839 

0.832 

0.824 

0.817 

0.81 

0.803 

0.796 

0.787 

0.781 

B.T.U  

3°-9 

31.2 

31-5 

31-7 

32 

32-3 

32.6 

33-° 

33-2 

The  last  line  shows  the  proper  assignment  of  thermal  units 
for  this  condition.  For  simplicity  both  y  and  yt  are  assumed 
to  vary  uniformly,  but  other  variations  can  be  worked  out  with 
a  little  more  trouble.  Evidently  the  sum  of  the  figures  in  the 
last  line  should  be  equal  to 

9  X  32  =  288; 

it  is  a  trifle  larger  in  the  table. 

Now  it  is  probable  that  the  best  values  of  the  factor  for  friction 
and  resistance  are  to  be  derived  from  investigations  on  turbines 
rather  than  from  separate  experiments  on  nozzles  and  vanes, 
and  it  is  evident  that  the  use  of  the  methods  of  representing 
the  friction  by  a  factor  y  is  rather  a  crude  way  of  trying  to  attain 
in  a  new  design  favorable  conditions  found  in  a  turbine  already 
built. 

Since  the  general  conditions  of  this  problem  are  the  same  as 
those  on  page  481,  the  efficiency  due  to  adiabatic  action  will  be 
the  same  as  is  also  the  efficiency  due  to  the  angles  and  velocities. 
Taking  the  factors  for  friction  in  the  guides  and  blades  as  each 


PRESSURE   COMPOUNDING 


499 


o.i,  the  corresponding  factors  are  0.9  and  0.9.  The  efficiency 
due  to  velocities  is  0.75,  and  the  mechanical  efficiency  may  be 
estimated  as  0.9.  The  combined  efficiency  of  the  turbine  is 

0.262  X  0.75  X  0.9  X  0.9  X  0.9  =  0.143. 

A  computation  like  that  on  page  483  with  this  efficiency  gives 
for  the  probable  steam  consumption  16.2  pounds  per  brake 
horse-power  per  hour. 

Assume  that  the  turbine  is  to  deliver  500  brake  horse-power; 
then  the  steam  consumption  per  second  will  be 

1 6. 2  X  500  4-  3600  =  2.25  pounds. 

We  can  now  determine  the  principal  dimensions  of  the  turbine 
to  suit  the  conditions  of  its  use.  Suppose  that  it  is  desired  to 
restrict  the  revolutions  to  1200  per  minute  or  20  per  second  ; 
then  with  nine  stages  and  a  peripheral  velocity  of  520  for  the 
vanes  the  diameter  will  be 

520  •*•  207T  =  8.28  feet. 

For  a  turbine  of  the  power  assigned  this  diameter  will  be 
found  to  be  inconveniently  large.  If,  however,  the  number  of 
stages  can  be  made  36,  the  velocity  will  be  reduced  to  260  feet 
per  second  as  computed  on  page  495.  This  will  give  for  the 
diameter 

260  -*-  207T  =4.14  feet. 

The  remainder  of  our  calculation  will  be  carried  out  on  these 
assumptions,  namely,  that  the  power  is  to  be  500  brake- 
horse-power,  and  that  there  are  to  be  36  stages.  If  the  method 
of  the  table  on  page  497  were  applied  to  a  turbine  having  the 
full  36  stages  now  contemplated,  it  would  have  37  lines;  namely, 
the  ten  already  set  down,  and  three  intermediate  entries  between 
each  pair  of  consecutive  lines;  but  the  temperatures  found  in 
that  table  would  be  found  in  the  more  extended  table  together 
with  their  specific  volumes.  We  can,  therefore,  use  that  table  to 
calculate  areas  and  lengths  of  vanes  for  9  out  of  the  36  stages, 


500 


STEAM-TURBINES 


10' 


FIG.  in. 


which  will  suffice  for  illustration.     Beginning  with  the  lowest  stage 

the  area  to  be  supplied  will  be 

2.25  X  157.4  -*•  600  =  0.590  square  feet; 

where  600  is  the  velocity  of  the  jet  computed  on  page  495. 
The  circumference  of  a  circle  having  the  diameter  of  4.14  feet 

is  13  feet;  but  of  this  a  portion,  one-fourth  or  one-third,  must  be 

assigned  to  the  thickness  of  the  guides.     If  we  take  one-fourth 

in  this  case  the  effective  perimeter 
becomes  9.75  feet.  But  as  is  evi- 
dent from  Fig.  in  the  peripheral 
space  assigned  to  the  distance 
between  guides  must  be  multiplied 
by  sin  a  in  order  to  find  the  effec- 
tive opening.  As  a  is  taken  to  be 
30°,  the  sine  is  one-half,  so  that  the 
total  width  of  spaces  between 
guides  is  reduced  to  4.88  feet.  The 

radial  length  of  the  guides  for  the  last  stage  will  consequently  be 
0.590  -T-  4.88  =  o.i 21  of  a  foot  =  1.45  inches, 

provided  that  there  is  full  peripheral  admission  to  the  guides. 

Now  the  angles  for  this  case  are  the  same  as  those  on  page  481 
and  /?  is  49°  10'.     Consequently  the  relative  velocity  is 
V2  =  V1  sin  a  -*-  sin  /?  =  600  sin  30°  -H  sin  49°  10'  =  397  feet. 

If  the  passages  between  the  vanes  are  made  of  constant  width, 
as  shown  in  Fig.  in,  the  effective  perimeter  will  be  the  entire 
perimeter  of  the  wheel  less  the  allowance  for  thickness.  An 
allowance  like  that  for  the  guides  will  make  the  vanes  shorter 
than  the  guides  in  this  case.  Let  us  try  making  the  thickness 
equal  to  a  space;  then  the  effective  perimeter  will  be  6.5  feet.  If 
the  density  of  the  steam  is  assumed  to  be  constant  for  a  given 
stage,  then  the  lengths  of  the  guides  and  vanes  will  be  inversely 
as  the  product  of  the  velocities  by  the  effective  perimeters,  so 
that  the  length  of  the  vane  will  be 
600  X  4.88 


i.45  X 


397  X  °-5 


=  1.65  inches. 


LEAKAGE  AND  RADIATION  501 

Conversely,  if  desired,  the  thickness  of  the  vanes  could  be 
adjusted  to  give  the  same  length.  Such  a  construction  as  this 
leads  to  is  likely  to  give  too  sharp  a  curvature  to  the  backs  of 
the  vanes,  and  it  may  be  better  to  give  only  the  thickness 
demanded  for  strength  and  take  the  chance  that  the  passage 
between  the  vanes  shall  not  be  filled.  If  allowance  is  made  for 
friction  and  the  consequent  reduction  in  velocity  the  lengths  of 
the  vanes  should  be  correspondingly  increased. 

The  lengths  of  the  guides  for  the  other  stages  will  be  directly 
proportional  to  the  specific  volumes  in  the  table  on  page  497, 
because  the  velocities  have  been  made  the  same  for  all  the  stages. 
For  example,  at  199°  the  length  for  full  admission  will  be 


77  O 

i-45  X  31.9  -5-  157  =  0.295  inch, 


which  will  be  the  proper  length  for  the  twenty-fourth  stage.  If 
it  is  considered  undesirable  to  further  reduce  the  length  we  may 
resort  to  admitting  steam  through  guides  for  only  a  portion  of 
the  periphery.  Making  the  arc  of  admission  vary  as  the  specific 
volumes,  the  fourth  stage  (line  i  of  the  table  on  page  497)  will 
have  admission  for 

360  X  3.93-^31.9-44°. 

Intermediate  lengths  of  vanes  and  arcs  of  admission  may  be 
computed  by  filling  out  a  table  like  that  on  page  497  for  all  the 
stages,  or  a  diagram  may  be  drawn  from  which  the  required 
information  can  be  had  by  interpolation;  the  values  on  the  line 
numbered  o  are  for  this  purpose,  there  being  of  course  no  corre- 
sponding stage.  In  fact  the  method  of  computing  at  convenient 
intervals  and  interpolating  from  curves  is  likely  to  be  more  accu- 
rate as  well  as  more  convenient,  as  the  error  of  adiabatic  calcula- 
tions for  steam  with  small  change  of  temperature  is  liable  to  be 
excessive. 

Leakage  and  Radiation.  —  This  type  of  turbine,  as  will  be  seen 
in  the  description  of  the  Rateau  turbine,  has  a  number  of  wheels 
each  in  its  own  chamber,  and  the  chambers  are  separated  by 
stationary  disks  that  extend  to  the  shaft.  Reduction  of  leakage 
must  be  attained  by  a  small  clearance  between  the  disk  and  the 


502 


STEAM-TURBINES 


shaft  for  a  proper  bearing  or  stuffing  box  cannot  be  placed  in  so 
inaccessible  a  place.  The  leakage  can  be  estimated  by  aid  of 
Rankine's  equation  on  page  432  or  from  Rateau's  experiments 
on  page  433 ;  but  both  methods  are  likely  to  give  results  that  are 
too  large,  and  a  factor  less  than  unity  should  be  applied;  but 
the  value  of  such  a  factor  for  a  long,  narrow,  annular  passage  is 
not  known,  and  any  estimate  must  be  crude.  For  a  turbine  of 
the  Rateau  type  the  leakage  is  likely  to  be  less  than  five  per  cent 
at  the  high  pressure  end.  Now  the  leakage  is  proportional 
nearly  to  the  difference  of  pressure  between  successive  chambers, 
and  as  the  difference  decreases  so  also  does  the  leakage  till  it 
becomes  of  no  account  at  the  lower  end.  To  allow  for  leakage 
the  length  of  guides  or  the  arc  of  admission  may  be  increased  at 
the  high  pressure  end  of  the  turbine.  There  does  not  appear 
to  be  any  information  concerning  the  radiation  from  steam- 
turbines.  On  the  one  hand  the  area  of  radiating  surface  is 
larger  than  for  steam-engines  and  on  the  other  the  temperatures 
are  less  for  the  greater  part  if  not  all  of  that  area.  For  compact 
steam-engines  the  radiation  is  likely  to  be  from  five  to  ten  per 
cent.  For  turbines  of  the  Rateau  and  Curtis  types  the  effect 
of  radiation  is  to  require  larger  areas  in  guides  and  passages 
at  the  high  pressure  end. 

Lead.  —  Turbines  with  pressure-compounding  usually  have 
some  space  between  the  vanes  of  one  wheel  and  the  next 
set  of  guides  or  nozzles,  and  consequently  the  absolute  exit 
velocity  is  mainly  if  not  entirely  dissipated,  so  that  the  steam 
enters  those  nozzles  with  no  appreciable  velocity.  If  this  action 
is  complete  it  would  appear  to  be  of  little  consequence  where  the 
guides  or  nozzles  are  placed.  Nevertheless  considerable  impor- 
tance is  attached  to  locating  the  guides  so  that  steam  from  the 
wheel  shall  flow  directly  into  them.  Clearly,  as  it  takes  an 
appreciable  time  to  flow  through  the  passages  between  the 
vanes,  the  steam  will  be  discharged  at  some  distance  from  the 
place  at  which  it  was  received  and  the  general  path  of  the  steam 
is  a  spiral  wound  around  the  turbine  case  in  the  direction  of 
rotation. 


RATEAU   TURBINE 


503 


Let  abcde  represent  a  vane  which  has  steam  entering  it 
tangentially  with  the  velocity  F2,  while  it  has  itself  the  velocity 
V.  Assuming  that  the  relative  velocity  is 
constant  we  may  divide  the  curve  into  a 
number  of  equal  small  parts  that  are  approxi- 
mately  straight.  From  b  lay  off 

v 


bV  =  ab 


FIG.  112. 


then 


will  be  a  point  in  the  trajectory  of  the  particle  of  steam. 

y 
In  like  manner  cc'  =  zab  —  ,  etc. 

*2 

The  path  aVtfd'e?  may  be  taken  as  the  trajectory  of  the  steam,  and 
ee?  is  the  lead  as  defined  above.  Properly  a  similar  construction 
should  be  made  also  for  the  back  of  the  vane,  and  the  mean  path 
should  be  taken  to  establish  the  lead.  Extreme  refinement  is 
probably  neither  necessary  nor  justifiable  in  this  work. 

Rateau  Turbine.  —  The  construction  of  this  turbine,  which  is 
Casing  of  the  pure  pressure-compound 

type  is  represented  by  Fig.  113, 
which  is  a  half  section  through 
the  shaft,  wheels  and  casing. 
The  wheels  are  light  dished 
plates  which  are  secured  to 
hubs  that  are  pressed  onto  the 
shaft  and  which  carry  the 
moving  vanes.  The  chambers 
are  separated  by  diaphragms 
of  plate  steel,  riveted  to  a  rim 
and  to  a  hub  casting.  The 
hubs  are  bushed  with  anti- 
friction metal  that  is  expected 
to  wear  away  if  it  by  chance 
touches  the  shaft.  This  tur- 
bine is  sometimes  divided  into 
two  sections  to  provide  a  middle  bearing  for  the  shaft,  which 
has  considerable  length  and  should  preferably  have  a  small 


STEAM-TURBINES 

diameter  to  reduce  leakage.  The  high  pressure  portion  may 
have  a  smaller  diameter  to  facilitate  arrangement  of  guides  and 
vanes.  Sometimes  t'here  are  three  diameters  for  the  same  pur- 
pose. But  little  extra  complication  of  computation  is  introduced 
by  such  change  of  diameter;  all  that  is  necessary  is  to  make 
the  portion  of  available  heat  per  stage  larger  in  proportion  to 
the  increase  in  peripheral  speed. 

TESTS   ON   RATEAU  TURBINE. 
DR.  A.  STODOLA.* 


Duration  minutes   

40 

5° 

2C? 

1  80 

3O 

Revolutions  per  minute      

2184 

2181 

oo 
2190 

2IOI 

o 

2200 

Steam  pressure  at  stop  valve  absolute 

pounds 

176  .  i 

1  7r    j 

1  7O    ^ 

168.4 

181.  i 

Superheating  degrees  F. 

52 

-1  /  j  •  A 

A  /  w  •  j 
14  8 

2O 

14.    6 

Steam  pressure  at  first  guides    .... 

44-7 

63-9 

-L*T  '  ^ 

95-4 

II9.9 

IT-  •  w 

J43-7 

Superheating  degrees  F  

32.6 

32.2 

20.9 

18.9 

17.1 

Absolute  exhaust  pressure      

1.29 

i-33 

i-5i 

I  .64 

1.89 

Effective  power   

172 

257 

417 

531 

634 

Steam  per  horse-power  per  hour,  ex- 

clusion of  air-pump    

19.0 

17.6 

15-7 

I5.6 

15-2 

The  accompanying  table  gives  results  of  tests  on  a  Rateau 
turbine  by  Professor  Stodola.  To  compare  with  results  from 
steam-engines,  these  latter  should  be  referred  to  brake  horse- 
power, with  a  mechanical  efficiency  of  0.85  to  0.90. 

This  type  of  turbine  has  been  applied  successfully  to  use 
exhaust  steam  from  reciprocating  engines  which  for  some  purpose 
exhaust  at  atmospheric  pressure  or  into  a  poor  vacuum.  Such 
application  can,  however,  be  but  local  or  accidental. 

Steam  Friction  of  Rotating  Disks.  —  The  resistance  which  a 
turbine  wheel  experiences  while  rotating  in  steam  can  be  divided 
into  two  parts :  first,  that  due  to  the  friction  of  the  smooth  disk, 
and  second,  that  due  to  the  action  of  the  vanes,  which  have  an 
effect  comparable  to  that  of  a  centrifugal  pump. 

From  a  consideration  of  tests  made  by  Odell  f  on  cardboard 
disks,  and  by  Lewecki  J  on  a  de  Laval  turbine  wheel  driven  in 

*  Steam  Turbines,  trans.  Dr.  L.  C.  Lowenstein. 

t  Engineering,  January,  1904.         \  Zeitschr.  d.  V.  deutsch  Ing.,  1903. 


SIDE   THRUST  505 

its  casing,  and  from  tests  of  his  own,  Professor  Stodola  gives  the 
following  equations  for  the  horse-power  required  to  drive  smooth 
wheels  and  to  drive  wheels  with  vanes  forward: 
Smooth  wheels 

H.P.  =0.02295  a.  D2'5  (—}\. 
Vioo/ 


Wheels  with  vanes 

V_ 
joo 


H.P.  =  [0.02295  a^D2'*  +  1.4346  a2L1'25]  (- 


where  D  is  the  diameter  in  feet,  L  is  the  blade  length  in  inches, 
V  is  the  peripheral  speed  in  feet  per  second,  and  7  is  the  density 
of  the  medium.     The  values  of  the  other  factors  are 
al  =  3.14  a2  =  0.42. 

These  formulae  explain  why  the  backing  turbine  for  marine 
propulsion  is  always  run  in  a  vacuum  when  idle. 

Turbines  which  have  only  a  partial  admission  must  be  affected 
by  some  such  action  for  that  part  of  the  revolution  during  which 
steam  is  not  admitted;  but  this  matter  is  obscure  and  such  a 
resistance  must  be  combined  with  friction  and  other  resistances. 
It  is  therefore  very  difficult  to  assign  the  proper  value  to  the  fric- 
tion factor  y  for  steam  in  the  vanes  or  in  the  guides  and  vanes  of 
a  velocity-compound  turbine.  In  particular  any  change  of  the 
angle  7  (Fig.  103,  page  480)  to  avoid  end  thrust  must  be  made 
with  caution  and  should  be  checked  by  experiment. 

Side  Thrust.  —  If  admission  is  restricted  to  only  a  part  of  the 
periphery  of  a  turbine,  then  in  order  to  preserve  a  balance  and 
avoid  unnecessary  pressure  on  the  bearings  of  the  shaft,  the  arc 
of  admission  should  be  divided  into  two  equal  portions,  that  are 
diametrically  opposite.  Some  builders,  however,  prefer  to 
ignore  this  effect,  and  concentrate  the  admission  at  one  side, 
because  there  is  tendency  for  the  steam  to  spread  which  will  have 
double  the  effect  if  the  arc  is  divided  as  suggested.  The  amount 
of  side  thrust  can  be  estimated  from  the  powers  developed  at 
the  several  wheels,  having  partial  admission,  together  with  the 
dimensions  and  speed  of  revolutions,  making  allowance  of  course 
for  the  distribution  of  the  torque  over  an  arc  of  a  circle. 


506  STEAM-TURBINES 

Pressure  and  Velocity  Compounding.  —  A  favorable  combina- 
tion may  be  made  of  the  two  methods  of  compounding  already 
discussed;  that  is,  the  pressure  and  temperature  range  may  be 
divided  between  two  or  more  chambers  in  each  of  which  shall  be 
two  or  three  sets  of  moving  vanes.  This  has  been  done  on  a 
large  scale  with  the  Curtis  turbine  which  appears  to  have  a  wider 
range  of  economical  application  than  any  other  type. 

Since  the  principles  of  each  method  have  been  discussed 
already,  we  will  illustrate  the  application  to  a  comparatively 
simple  problem  avoiding  too  great  minutiae  of  detail. 

Let  us  take  for  the  principle  conditions  the  delivery  of  500  kilo- 
watts of  electrical  energy,  which,  with  an  efficiency  of  the  dynamo 
of  about  0.87,  will  correspond  to  nearly  770  brake  horse-power. 

Let  the  initial  pressure  be  150  pounds  by  the  gauge,  and  the 
vacuum  be  28  inches  of  mercury.  Let  the  angle  of  the  nozzles 
be  a  =  20°.  The  absolute  pressures  will  be  about  165  pounds 
and  one  pound  absolute,  and  the  compounding  temperatures 
are  366°  and  102°  F.  Dry  saturated  steam  at  the  given  pressure 
will  have  nearly  1.56  units  of  entropy,  and  for  this  the  temperature- 
entropy  table  gives  for  adiabatic  expansion  with  the  above  limits 
of  temperature  the  heat  contents  as  1193  and  871.  The  value 
of  q2  is  70  at  the  lower  temperature;  and  consequently  #/2 
is  equal  to  801  B.T.U. 

The  thermal  efficiency  of  adiabatic  expansion  without  allowing 
for  any  losses  is 

xjr~                       801  00 

e  =  i — *-* =  i =  0.288; 

ri  +  ?i  ~  ft  II25 

the  corresponding  heat  consumption  is 

42.42  -f-  0.288  =  147  B.T.U. 

per  horse-power  per  minute. 

The  efficiency  for  the  turbine  without  friction  by  equation 
(291),  page  481  is 

e  =  cos2  a  =  0.883. 

The  efficiency  of  the  nozzles  has  already  been  determined  to  be 
0.85  by  the  selection  of  0.15  for  y.     Let  us  further  assume  that 


PRESSURE   AND   VELOCITY   COMPOUNDING  507 

the  combined  effect  of  losses  in  the  vanes  may  be  taken  to  be 
equivalent  to  making  y0  equal  to  25  so  that  i  —  yQ  is  0.75;  this 
is  in  effect  the  efficiency  factor  for  the  vanes  as  affected  by  friction. 
If,  further,  we  take  the  mechanical  efficiency  of  the  machine  as 
0.9,  then  the  combined  efficiency  for  the  turbine  will  be 

0.288  X  (0.883  X  °-85  x  °-75)  x  0.9  =  0.144. 
This  corresponds  to 

42.42  -r-  0.144=  295  B.T.U. 

per  horse-power  per  minute.  Now  it  costs  to  make  steam  from 
water  at  102°,  and  at  an  absolute  pressure  of  165  pounds,  1125 
(r1  +  ql  -  q2)  thermal  units,  as  already  calculated  in  the  deduc- 
tion of  the  efficiency  of  adiabatic  action.  Consequently  the  steam 
per  horse-power  per  hour  will  be 

295  X  60  -T-  1125  =  15.7 

pounds  per  brake  horse-power  per  hour.  To  this  should  properly 
be  added  a  fraction,  to  allow  for  leakage  and  radiation,  amounting 
to  five  or  ten  per  cent;  this  added  amount  of  steam  will  affect 
the  size  of  the  high  pressure  nozzles  only  in  this  case,  and  as 
extra  nozzles  are  sure  to  be  provided  we  will  take  no  further 
account  of  it  than  to  say  that  the  steam  consumption  may  amount 
to  16.5  to  17.3  pounds  per  brake  horse-power  per  hour. 

The  heat  contents  which  have  already  been  found  give  for  the 
adiabatic  available  heat 

I][93  -  87J  =  322> 

and  if  this  be  divided  equally  we  have  161  thermal  units  per 
stage.  Using  0.15  for  y  in  the  nozzles,  the  velocity  of  the  jet 
becomes 

V  =\/2  X  32.2  X  778  X  161  Xo.Ss  =2610 

feet  per  second. 

Assuming  that  we  may  use  three  sets  of  moving  vanes  the 
velocity  for  them  will  be 

2610  -i-  (2  X  3)  =  435 
feet  per  second. 


508  STEAM-TURBINES 

If  we  choose  a  diameter  of  4^  feet  for  the  pitch  surface  of  the 
vanes  it  will  lead  to  the  use  of  1850  revolutions  per  minute. 

To  find  the  intermediate  pressure  we  may  take  for  the  heat 
contents  at  that  pressure 

1193  -  161  =  1032, 

which  in  the  temperature-entropy  table  corresponds  to  223°  F., 
or  18.2  pounds.  Since  the  back-pressure  for  the  nozzles  is  rela- 
tively small  in  each  case,  the  nozzles  will  have  throats  for  which 
the  velocities  must  be  determined  in  order  to  find  the  areas. 
The  throat  pressures  may  be  taken  to  be 

165  X  0.58  =  95.7;     18.2  X  0.58  =  10.6, 

and  the  corresponding  temperatures  are  325°  and  196°  F. 

Since  the  rounding  of  the  nozzle  is  likely  to  give  but  small 
area  for  friction  compared  with  the  cone  for  expanding  to  the 
back-pressure,  we  may  assume  adiabatic  expansion  to  the  throat 
and  allow  the  entire  value  of  y  =  0.15  for  the  computation  for 
the  exit.  This  appears  to  agree  with  tests  showing  that  such 
nozzles  give  nearly  full  theoretical  discharge.  The  heat  contents 
by  the  temperature-entropy  table  at  entropy  1.56  and  325°  F. 
amounts  to  1150  B.T.U.,  the  value  of  x  is  0.960  and  the  specific 
volume  is  4.41  cubic  feet.  The  apparent  available  heat  is 


-  ii5°=43B.T.u. 
giving  a  throat  velocity  of 


V  =  \/2  X  32.2  X  778  X  43  =  1470. 

The  apparent  available  heat  for  producing  velocity  at  the  exit 
with  y  taken  at  0.15  is 

0.85  X  161  =  137  B.T.U., 
leaving  for  the  heat  contents 

1193  —  137  =  1056  B.T.U. 

The  heat  of  the  liquid  is  191  so  that  with  963  for  r  we  have 
x'  =  x'r'  -v-  r'  =  (1056  —  191)  -v-  963  =  0.898. 


PRESSURE   AND    VELOCITY   COMPOUNDING  509 

The  specific  volume  is 

v  =  (xu  +  o)  =  0.898  (21.9  —  0.016)  +  0.016  =  19.7. 

With  15.7  pounds  of  steam  per  brake  horse-power  per  hour 
and  770  horse-power  the  steam  per  second  is 

•w  =  15.7  X  770  -7-  3600  =  3.36  pounds. 

The  combined  area  of  discharge  of  all  the  first  stage  nozzles 
is  therefore,  with  the  velocity  at  exit  equal  to  2610  feet, 

3.36  X  19.7  X  144  -7-  2610  =  3.65  square  inches. 

The  nozzles  of  turbines  of  this  type  are  sometimes  made  square 
at  the  exit  so  as  to  give  a  continuous  sheet  of  steam  to  act  on  the 
vanes.  If  the  side  of  such  a  nozzle  were  made  half  an  inch 
there  would  appear  to  be  fourteen  and  a  half  such  nozzles;  the 
turbines  would  probably  be  given  16  or  18  of  them,  which  could 
be  arranged  in  two  groups.  Since  the  angle  of  the  (nozzle  is  20° 
the  width  of  the  jet  measured  along  the  perimeter  of  the  wheel 
will  be 

0.5-7-  sin  20°  =0.5-7-  0.3420  =  1.46  inch. 

Allowing  one-fourth  of  the  width  of  the  orifice  for  the  thickness 
of  the  walls,  the  width  occupied  by  eight  nozzles  would  be 

1.46  X  1.25  X  8  =  14!  inches. 
The  combined  throat  area  of  all  the  nozzles  will  be 

3.36  X  4.41  X  144  -T-  1470  =  1.45  square  inch. 

Dividing  by   14 J,   the  number  of  necessary  nozzles,   gives  for 
the  throat  area  of  one  nozzle 

1.45  -5-  14.5  =  o.iooo  square  inch, 

so  that  the  diameter  will  be  about  0.36  of  an  inch. 

A  method  of  calculation  for  the  second  set  of  nozzles  consistent 
with  the  method  of  determining  the  intermediate  pressure  is  as 
follows:  The  pressure  in  the  throat  has  already  been  found  to 
be  10.6  pounds,  corresponding  to  196°  F.,  for  which  the  tem- 
perature-entropy table  at  1.56  units  of  entropy  gives  for  heat 


STEAM-TURBINES 

contents  998.  The  heat  contents  at  18.2  pounds  (223°)  has 
already  been  found  to  be  1032,  so  that  the  available  heat  for 
adiabatic  flow  appears  to  be  34  B.T.U.,  which  gives  for  the 
velocity  in  the  throat 

F  =  N/2  X  32.2  X  778  X  34  =  1300  feet. 

The  next  step  is  the  determination  of  the  qualities  at  the  throat 
and  exit,  and  from  them  the  specific  volumes.  Now  of  the 
161  B.T.U.  available  for  adiabatic  flow  in  the  first  nozzles  only 
a  part  has  actually  been  changed  into  work,  because  there  was 
allowed  0.15  for  friction  in  the  nozzle,  and  0.25  for  losses  in  the 
guides  and  vanes,  while  the  efficiency  due  to  angles  and  velocities 
was  0.883.  The  heat  changed  into  work  was  therefore 

161  X  0.85  X  0.75  X  0.883  =  9°-6  B.T.U. 

Consequently  the  heat  left  in  the  steam  as  it  approaches  the 
second  nozzle  is 

1193  —  91  =  1 102  B.T.U. 

per  pound.  Now  r  has  the  value  963  at  223°  F.,  and  q  is  191,  so 
that  the  quality  is 

X=   (lI02    —    I9l)    -r-   963  =  0.946. 

In  the  flow  from  the  entrance  to  the  throat  34  B.T.U.  are 
assumed  to  be  changed  into  kinetic  energy  leaving  for 

xr  +  q  =  1 102  —  34  =  1068, 

and  as  r  is  equal  to  980  and  q  is  164  at  196°  F.,  we  have 
x  =  (1068  —  164)  -T-  980  =  0.923 

at  the  throat  of  the  second  nozzle. 

Allowing  as  before  0.15  for  the  friction  of  the  nozzle  there  will 
be 

0.85  X    l6l   =    137  B.T.U. 

changed  into  kinetic  energy  for  the  entire  nozzle  leaving 

xr  +  q  =  1 102  —  137  =  965  B.T.U.; 
and  at  i  pound  or  102°  F.,  the  values  of  r  and  q  are  1035  and  70 

X    =     (965    -    70)    -r-    1035    =    0.865. 


PRESSURE  AND  VELOCITY    COMPOUNDING  511 

at  exit  from  the  second  set  of  nozzles.  The  volume  of  saturated 
steam  at  102°  is  332  cubic  feet,  and  with  x  equal  to  0.865  the 
specific  volume  is  287  cubic  feet.  Consequently,  with  a  weight  of 
3.36  pounds  per  second,  and  a  velocity  of  2610  feet,  the  united 
areas  of  all  the  nozzles  at  exit  will  be 

3.36  X  287  X  144  -^  2610  =  53.2  square  inches. 

Now  the  perimeter  of  a  circle  having  a  diameter  of  4^  feet  is 
about  170  inches.  Allowing  for  the  sine  of  the  angle  20°  and 
one-fourth  for  thickness  of  guides  there  will  be  about  43.5  inches 
for  the  united  width  of  passages  between  guides  so  that  the 
radial  length  will  be 

53-2  +  43-5  =  1-22  inch. 

The  specific  volume  of  saturated  steam  at  197°  is  35.6  cubic 
feet,  so  that  with  x  equal  to  0.923  the  specific  volume  is  32.9. 
Now  the  areas  are  proportional  to  the  specific  volumes  and 
inversely  as  the  velocities,  consequently  the  length  of  guides  at  the 
throat  is 

i.aa  X  222  x  3*2  _aa8  inch. 

1300  287 

The  length  of  the  vanes  and  guides  can  be  found  by  the  method 
on  page  500,  using  relative  velocities  for  the  vanes  and  absolute 
velocities  for  the  guides.  The  velocities  decrease  as  indicated 
by  Fig.  107,  page  487,  and  the  lengths  must  be  correspondingly 
increased.  In  this  case,  however,  there  are  two  considerations 
which  influence  the  lengths  that  should  be  finally  assigned  to  the 
guides  and  vanes,  (i)  The  thickness  may  be  diminished,  which 
tends  to  decrease  the  length.  (2)  Friction  reduces  the  velocity 
which  tends  to  increase  the  length.  Friction  of  course  diminishes 
all  velocities  including  the  peripheral  velocity  of  the  wheel,  but  a 
proper  discussion  of  that  matter  would  be  both  long  and  uncertain. 

Attention  has  already  been  called  to  the  defect  of  this  method 
of  making  all  the  calculations  at  a  single  value  of  entropy  and 
trying  to  allow  for  friction  and  other  losses  by  simple  factors. 
The  difficulty  is  aggravated  in  this  case  by  the  fact  that  the 


5I2 


STEAM-TURBINES 


second  set  of  nozzles  or  guides  have  proper  throats.  The  proper 
method  after  having  selected  a  set  of  intermediate  pressures 
appears  to  be  to  calculate  the  turbine  step  by  step.  The  steam 
supplied  to  the  second  set  of  nozzles  (or  guides)  has  been  found 
to  have  the  quality  0.946,  and  this  is  probably  a  good  approxima- 
tion to  the  actual  condition,  even  if  allowance  is  made  for  radi- 
ation and  leakage.  The  temperature-entropy  table  gives  for 
steam  having  that  quality  and  the  temperature  223,  the 
entropy  as  nearly  1.66.  At  that  entropy  the  heat  contents  at 
the  initial,  throat  and  exit  pressures,  are  given  in  the  following 
table  with  also  the  quality  and  specific  volume  at  the  throat; 
the  table  also  gives  the  quality  and  specific  volumes  at  exit  with 
y  equal  to  0.15. 


Pressure. 

Temperature. 

Heat  contents. 

Quality. 

Specific  volume. 

18.2 

223 

IIOO 

0.94 

10.6 

196 

1063 

0.92 

33-3 

I  .0 

102 

927 

0.86 

286 

The  apparent  available  heat  for  adiabatic  flow  to  the  throat 
is  now 

noo  -  1063  =  37, 

which  would  give  a  velocity  of 

V  =  V2  X  32.2  X  778  X  37  =  1360, 

instead  of  1280  as  previously  found.     The  apparent  available 
heat  to  the  exit  with  0.15  for  the  friction  factor  is  now 

(noo  -  927)0.85  =  147, 
which  gives  for  the  exit  velocity 

V  =  V2  X  32.2  X  778  X  147  =  2710, 

instead  of  2610  previously  computed. 

This  comparison  shows  that  the  intermediate  pressure  deter- 
mined by  the  customary  method  will  be  too  high,  and  that  to 
obtain  the  desired  distribution  of  temperature  the  factors  for 


CURTIS   TURBINE 


513 


the  lower  stages  must  be  modified  arbitrarily  as  may  be  deter- 
mined by  comparison  with  practice. 

Curtis  Turbine.  —  Fig.  114  shows  a  partial  elevation  and  section 
of  the  essential  features  of  a  Curtis  turbine,  which  has  four 
chambers  and  two  sets  of  moving  vanes  in  each  chamber.  The 
axis  of  the  turbine  is  vertical  which  demands  an  end  bearing, 
the  difficulties  of  which  construction  appear  to  have  been  met  by 


FIG.  114. 

pumping  oil  under  pressure  into  the  bearing,  so  that  there  is 
complete  lubrication  without  contact  of  metal  on  metal.  The 
condenser  is  placed  directly  under  the  turbine,  and  the  electric- 
generator  is  above  on  a  continuation  of  the  shaft.  The  arrange- 
ment appears  to  be  convenient,  and  in  particular  to  demand 
small  floor  space  only. 

When  used  for  marine  propulsion  the  Curtis  turbine  has  a 
horizontal  shaft  from  necessity,  and  has  a  large  number  of  stages. 


514 


STEAM-TURBINES 


A  turbine  developing  8000  horse-power  has  seven  pressure 
stages,  each  of  which  but  the  first  has  three  velocity  stages,  that 
one  has  four  velocity  stages.  The  diameter  is  ten  feet  and 
the  peripheral  velocity  is  180  feet  per  second. 

Tests  on  Curtis  Turbines.  —  The  following  tables  give  tests 
on  two  Curtis  turbines,  having  two  and  four  pressure  stages, 
respectively;  both  were  made  by  students  at  the  Massachusetts 
Institute  of  Technology. 

TESTS  ON   A   TWO-STAGE   CURTIS   TURBINE. 
DARLING  AND  COOPER.* 


Duration  minutes 

I2O 

I2O 

I2O 

I2O 

60 

Throttle  pressure  gauge     

146.  ? 

I4C  .  7 

143  •  2 

143.9 

149  .  3 

Throttle  temperature  F. 

CJI2 

t?2O 

464 

SO2 

^12 

Barometer  inches    ...                ... 

20.8 

20  .0 

29.9 

29  .9 

3O.O 

Exhaust  pressure  absolute  pounds  .    . 
Load  kilowatts                                .    . 

0.82 

161  4 

0.79 
2CC     7 

0.92 
374-O 

0.84 
^12.0 

0.85 

731  .0 

Steam  per  kilowatt  hour,  pounds     .    . 
Thermal  units  kilowatt  minute     .    .    . 

21.98 
440 

19.63 
396 

19.98 
392 

18-43 
369 

17-75 

357 

If  the  efficiency  of  the  dynamo  is  taken  at  0.9  and  one  kilowatt 
is  rated  as  1.34  horse-power,  the  steam  and  heat  consumptions 
per  brake  horse-power  are,  for  the  best  result, 

1 1. 8  pounds  239  B.T.U. 

TESTS    ON    A   FOUR-STAGE    CURTIS   TURBINE 

COE    AND   TRASK.f 


Duration  minutes    

60 

60 

60 

1  80 

I2O 

Boiler  pressure,  pounds         .        ... 

1^2 

140   6 

IS2  .  I 

jro 

ICQ     4 

Vacuum  inches    

28.  < 

28.2 

28.8 

28.4 

28.3 

Load  kilowatts 

282 

380 

(T23 

<62 

788 

Steam  per  kilowatt  hour  pounds      .    . 

21.4 

20.3 

18.8 

IQ-5 

19-3 

Thermal  units  per  kilowatt  (minute)  . 

394 

37° 

352 

360 

357 

*  Thesis,  M.  I.  T.,  1905. 
t  Thesis,  M.  I.  T.,  1906. 


REACTION   TURBINES 


515 


Taking  the  efficiency  of  the  dynamo  as  0.9  and  a  kilowatt  as 
1.34  horse-power,  the  best  result  is  equivalent  to  a  steam  con- 
sumption of  12.6  pounds  and  a  heat  consumption  of  237  thermal 
units. 

Reaction  Turbines.  —  The  essential  feature  of  a  reaction 
turbine  is  a  fall  of  pressure  and  a  consequent  increase  of  veloc- 
ity in  the  passages  among  the  vanes  of  the  turbine.  Since 
such  wheels  commonly  are  affected  by  impulse  also  they  are 
sometimes  called  impulse-reaction  wheels,  but  if  properly  under- 
stood the  shorter  name  need  not  lead  to  confusion.  In  conse- 
quence of  the  feature  named  the 
relative  exit  velocity  F3  is  greater 
than  F2.  Another  consequence  is 
that  steam  leaks  past  the  ends 
of  the  vanes  which  are  usually 
open,  and  there  is  also  leakage 
past  the  inner  ends  of  the  guides 
which  are  also  open;  this  feature 
is  shown  by  Fig.  115. 

The  reaction  turbine  is  always 
made  compound  with  a  large 
number  of  stages,  one  set  of  guides 
and  the  following  set  of  vanes 
being  counted  as  a  stage.  In 
consequence  the  exit  pressure  either 
from  the  guides  or  the  vanes  is 

only  a  little  less  than   the  entrance  pressure,  and  the  passages 
are  all  converging. 

There  is  no  axial  thrust  because  there  is  no  change  in  velocity 
of  flow;  f  is  commonly  equal  to  the  exit  angle  a  from  the  guides. 
A  common  value  for  these  angles  is  20°. 

The  guides  and  vanes  follow  alternately  in  close  succession 
leaving  onjy  the  necessary  clearance;  the  kinetic  energy  due  to 
the  absolute  exit  velocity  from  a  given  set  of  vanes  is  not  lost  but 
is  available  in  the  next  set  of  guides.  The  turbines  are  usually 


FIG.  115. 


516  STEAM-TURBINES 

made  in  two  or  three  sections  as  shown  by  Fig.  117,  page  526, 
and  it  is  only  at  the  end  of  a  section  that  the  kinetic  energy  due 
to  the  absolute  exit  velocity  is  rejected;  at  the  end  of  a  section 
this  kinetic  energy  is  changed  into  heat  and  is  in  a  manner 
available  for  the  next  section;  at  the  end  of  the  turbine  it  is  of 
course  wasted.  Since  there  are  usually  sixty  stages  or  more 
the  influence  of  the  kinetic  energy  rejected  is  likely  to  be  less 
than  five  per  cent  and  it  may  properly  be  combined  with  the 
general  factor  to  allow  for  friction  and  leakage  past  the  ends  of 
the  guides  and  vanes.  Both  influences  reduce  the  change 
of  heat  into  work  applied  to  the  turbine  and  increase  the 
value  of  the  quality  x  and  also  of  the  specific  volume  of  the 
mixture  of  steam  and  moisture. 

Since  the  exit  absolute  velocity  from  the  vanes  is  applied  to 
driving  the  steam  into  the  next  set  of  guides,  there  is  no  direct 
advantage  in  avoiding  velocity  of  whirl  at  this  place;  it  is  only 
necessary  to  give  the  guides  the  proper  angle  at  entrance  to 
receive  the  steam.  Indirectly  it  is  disadvantageous  to  have  a 
high  velocity  at  the  entrance  to  the  guides,  or,  for  that  matter,  in 
any  part  of  the  turbine,  as  the  friction  is  probably  proportional 
to  the  square  of  the  velocity  as  has  been  assumed  in  the  use  of 
the  friction  factor  y. 

The  steam  enters  a  set  of  guides  with  a  certain  velocity,  i.e., 
the  exit  absolute  velocity  from  the  preceding  set  of  vanes. 
On  account  of  the  loss  of  pressure  in  the  guides  a  certain  amount 
of  heat  is  changed  into  kinetic  energy  and  the  equivalent  increase 
of  velocity  may  be  added  to  the  entrance  velocity  to  find  the 
exit  velocity  which  is  of  course  an  absolute  velocity.  This  abso- 
lute velocity  combined  with  the  velocity  of  the  blades  gives  the 
relative  entrance  velocity  to  the  vanes.  To  this  entrance  veloc- 
ity is  to  be  added  the  gain  in  velocity  due  to  change  of  heat  into 
kinetic  energy  in  the  vanes,  in  order  to  find  the  relative  exit 
velocity.  The  ratio  of  the  heat  used  in  the  vanes  to  that  used 
in  the  entire  stage  is  called  the  degree  of  reaction.  Commonly 
the  degree  of  reaction  is  one-half;  that  is,  the  amount  of  heat 
used  in  the  vanes  is  equal,  to  that  used  in  the  guides;  and 


CHOICE   OF   CONDITIONS 


517 


the   gain  of   velocity  in  the  vanes  is  equal  to  the  gain  in  the 
guides. 

In  Fig.  116  let  Vl  be  the  velocity  of  the  steam  leaving  the 
guides  and  V  the  velocity  of  the  vanes;  then  V2  is  the  relative 
velocity  of  the  steam  entering  the  vanes.  F3  is  the  relative  exit 
velocity  which  is  greater  than  V2  on  account  of  the  change  of 
heat  into  work.  V \  is  the  absolute  exit  velocity  from  the  vanes 
with  which  the  steam  enters  the  next  set  of  guides.  If  the  con- 
ditions for  successive  stages  are  the  same,  V±  is  also  equal  to  the 
entrance  velocity  to  the  set  of  guides  of  the  stage  under  discussion, 
and  if  ce  is  laid  off  at  ac'  then  c'b  is  the  gain  of  velocity  in  the 


FIG.  116. 


guides.  Consequently  to  construct  F3  we  may  lay  off  ce'  equal 
to  ac  and  efd  equal  to  c'b.  Now  a  and  y  are  commonly  made  equal, 
and  therefore  the  triangles  abc  and  cde  are  equal.  Consequently 
the  angle  &  for  the  entrance  to  the  guides  is  equal  to  /?  at  the 
entrance  to  the  vanes.  In  fact  the  guides  and  vanes  have  the 
same  form. 

Choice  of  Conditions.  —  The  foregoing  discussion  shows  that 
the  designer  is  given  a  wider  latitude  in  his  choice  of  conditions 
for  the  compound  reaction  turbines  than  appeared  possible 
for  impulse  turbines,  though  if  the  restriction  of  no  axial  thrust 
were  removed  from  the  latter  the  comparison  would  be  quite 
different. 


STEAM-TURBINES 


The  most  authoritative  statement  of  the  preferable  conditions 
in  practice  for  reaction  turbines  of  the  Parson's  type  is  formed 
in  a  paper  by  Mr.  E.  M.  Speakman,*  but  much  of  the  infor- 
mation in  the  hands  of  the  builders  "  being  based  on  long  and 
costly  experiments,  much  reticence  is  observed  regarding  their 
publication."  The  statement  of  practical  conditions  is  therefore 
based  on  such  information  as  can  be  gleaned  from  his  paper, 
with  obvious  applications  by  ordinary  methods.  Factors  for 
friction  and  leakage  are  largely  conjectural,  as  must  in  fact  be 
the  case  at  present  for  all  turbines,  and  for  our  purpose  may 
perhaps  be  limited  to  giving  the  student  an  idea  of  the  nature  of 
the  problems. 

The  ratio  of  the  velocity  of  the  vanes  to  the  velocity  of  the 
steam  has  varied  in  turbines  built  by  the  Parsons  Company 
from  0.25  to  0.85.  In  general  the  ratio  may  be  taken  as  0.6. 

These  turbines  are  usually  built  with  two  or  three  diameters 
of  the  revolving  cylinder  or  rotor  as  shown  in  Fig.  117.  The 
following  tables  give  the  practice  of  that  company  with  regard 
to  peripheral  speed  and  number  of  stages. 


PARSONS   TURBINES  —  ELECTRICAL  WORK. 


Peripheral  speed,  feet  per  second. 

Normal  output 

Number  of 

Revolutions 

kilowatts. 

stages. 

per  minute. 

First  expansion. 

Last  expansion. 

5000 

135 

33° 

70 

75° 

35°° 

138 

280 

75 

I2OO 

2500 

125 

300 

84 

1360 

1500 

I25 

360 

72 

1500 

1000 

125 

250 

80 

I800 

750 

125 

260 

77 

2000 

500 

I2O 

285 

60 

3000 

250 

100 

210 

72 

3000 

75 

100 

200 

48 

4000 

*  Tram.  Inst.  Eng.  and  Shipbld.,  Scot.,  vol.  xlxix,  1905-06. 


CHOICE   OF   CONDITIONS 


PARSONS  TURBINE  —  MARINE   WORK. 


Type  of  vessel. 

Peripheral  speed,  feet 
per  second. 

Ratio  of 
velocities, 
vanes  to 

Number 
of 

H.P. 

L.P. 

steam. 

High  speed  mail  steamers    

70-80 

110-130 

°-45-°-5 

4 

Intermediate  mail  steamers      .... 

80-90 

UO-I35 

0.47-0.5 

3-4 

Channel  steamers  

90-105 

120-150 

0.37-0.47 

3 

Battleships  and  large  cruisers      .    .    . 

85-100 

"5-135 

0.48-0.52 

4 

Small  cruisers     

105-120 

130-160 

0.47-0.5 

3-4 

Torpedo  crafts   .        

110-130 

160-210 

0.47-0.51 

3-4 

The  Westinghouse  Company  have  used  much  higher  veloc- 
ities of  vanes  for  electrical  work  than  given  in  the  above  tables ; 
as  much  as  170  feet  per  second  for  the  smallest  cylinder  and 
375  for  the  largest  cylinder. 

The  blade  height  should  be  at  least  three  per  cent  of  the 
diameter  of  the  cylinder  in  order  to  avoid  excessive  leakage 
over  the  tips.  Mr.  Speakman  says  that  leakage  over  the  tips 
of  the  blades  is  perhaps  not  so  detrimental  on  account  of  actual 
loss  by  leakage  as  because  it  upsets  calculations  regarding 
passages  by  increasing  the  steam  volume. 

The  following  equation  represents  Mr.  Speakman's  diagram 
for  clearances  over  tips  of  vanes, 


clearance  in 
inches 


=  o.oi  +  0.008  diam.  in  feet. 


The  proportions  of  blades  may  be  taken  from  the  following 
table: 

PROPORTIONS   OF   BLADES  —  INCHES. 


Height  i 

Width 

Pitch  1 

Axial  clearance 


10 


12 

! 

2* 


1 8 


21 
I 

1 


24 


Mr.   Parsons  *  gives  for  the  efficiency  of  the  steam  in  the 
turbine  blades  themselves  0.70  to  0.80. 

*  7ns/.  Naval  Arch.,  1903. 


520  STEAM-TURBINES 

In  addition  to  the  leakage  past  the  tips  of  the  blades  which 
cannot  in  practice  be  separated  in  its  effects  from  friction, 
there  is  likely  to  be  a  considerable  leakage  past  the  balance 
pistons  which  will  be  described  in  connection  with  Fig.  117. 
This  leakage  is  in  the  end  direct  to  the  condenser,  and  no  account 
need  be  taken  of  it  in  the  design  of  the  blading  of  the  turbine; 
but  allowance  should  be  made  in  comparing  theoretical  calcula- 
tions with  results  of  tests. 

Design  for  a  Reaction  Turbine.  —  Let  us  take  for  the  principal 
conditions  the  delivery  of  500  kilowatts  of  electrical  energy,  which 
with  an  efficiency  of  the  dynamo  of  about  0.87  will  correspond 
to  770  brake  horse-power,  as  for  the  calculation  on  page  506.  Let 
the  initial  pressure  be  150  pounds  by  the  gauge,  and  the  vacuum 
be  28  inches.  The  absolute  pressures  corresponding  are  165 
pounds  and  one  pound,  and  the  temperatures  are  365°.9  and 
102°  F.  The  calculation  referred  to  gives  for  the  thermal 
efficiency  of  adiabatic  action  0.285,  which  corresponds  to 
149  B.T.U.  per  horse-power  per  minute.  If  we  allow  0.60  for 
the  turbine  efficiency,  and  ten  per  cent  for  leakage  to  the  con- 
denser and  radiation,  and  take  0.9  for  the  mechanical  efficiency 
we  shall  have  for  the  combined  efficiency  of  the  turbine 

0.288  X  0.60  X  0.9  X  0.9  =  0.140. 

This  will  give  for  the  heat  and  steam  consumption  per  horse- 
power, 16.3  pounds  per  hour  and  305  B.T.U.  per  minute.  These 
are  to  be  compared  with  results  of  tests  to  determine  whether 
the  constants  assumed  are  proper. 

For  the  estimate  of  the  weight  of  steam  to  be  used  in  deter- 
mining the  dimensions  of  the  turbine  we  should  omit  the  factor 
for  leakage  to  condenser  and  radiation,  which  will  give  for  the 
steam  per  horse-power  per  hour  14.7  pounds.  The  weight  of 
steam  per  second  to  be  used  in  computing  passage  therefore 
becomes 

w  =  14.7  X  770  -*-  3600  =  3.15  pounds. 

Let  the  peripheral  speed  of  the  smallest  cylinder  be  taken  as 
225  feet  per  second,  and  let  the  intermediate  and  low-pressure 


DESIGN    FOR  A    REACTION   TURBINE  521 

cylinders  be  i  J  and  2\  times  the  diameter  of  the  small  cylinders. 
Let  the  peripheral  speed  be  0.75  of  the  steam  velocity,  then  the 
latter  will  be  300  feet  per  second.  If  the  exit  angles  for  guides 
and  vanes  be  taken  as  20°  and  if  the  degree  of  reaction  is  0.5, 
the  velocities  and  angles  will  be  represented  by  Fig.  116,  page 
517.  In  that  figure 

gb  =  Vl  cos  20°  =  0.940  Vl  ; 
and  as  V  is  0.75  Vv 

we  have  gc  =  (0.940  —  0.75)  V1  =  0.190  Fr 

But  ag  =  Vl  sin  20°  =  0.342  Ft; 

and  tan  /?  =  0.342  -*-  0.190  =  1.800   .*.    /?  =  61°. 

The  angle  /?  is  given  to  the  backs  of  the  blades,  and  the  angle  at 
the  faces  is  somewhat  larger,  as  will  appear  by  Fig.  115,  page  515  ; 
in  consequence  there  is  some  impulse  at  the  entrance  to  the  vanes. 
To  get  the  relative  velocity  we  have 


+  &   =  (°-342    +  0.190)  V* 
.'•    V,  =  0.392  Vr 

But  it  is  shown  on  page  517  that  for  the  conditions  chosen  the 
increase  of  velocity  in  either  guides  or  vanes  is  equal  to 

Vl  -  V2  =  (i  -  0.392)  V1  =  0.608  X  300  =  182 

feet  per  second. 

Now  the  equation  for  velocity  when  h  thermal  units  are  avail- 
able is 

V  =  V2  X  32.2  X  778/1, 
and  conversely 

h  =  18?  •*-  (64-4  X  778)  =  0.661  B.T.U. 

This  is  the  amount  with  allowance  for  friction  and  leakage 
past  the  ends  of  the  blades  which  has  been  assigned  the  factor 
0.6,  so  that  for  the  preliminary  adiabatic  computation  we  may 
take  for  one  set  of  blades 

0.661  -?•  0.6  =  1.1  B.T.U., 


522 


STEAM-TURBINES 


and  for  a  stage,  consisting  of  a  set  of  guides  and  vanes,  we  may 
take  for  the  basis  of  the  determination  of  the  proper  number  of 
stages  2.2  B.T.U.  per  pound  of  steam  used. 

It  appears  on  page  507  that  adiabatic  expansion  from  165 
pounds  absolute  to  one  pound  absolute  gives  322  thermal  units 
for  the  available  heat.  If  this  is  to  be  distributed  to  the  stages 
of  a  turbine  with  2.2  units  per  stage,  then  the  total  number  of 
stages  will  be 

322  -5-  2.2  =  146 

stages.  This  is  under  the  assumption  that  the  turbine  has  a 
uniform  diameter  of  rotor  with  225  feet  for  the  velocity  of  the 
vanes;  we  have,  however,  taken  the  intermediate  diameter  ij 
times  the  high-pressure  and  the  low-pressure  2\  times.  The 
peripheral  velocities  will  have  the  same  ratios,  and  the  amounts 
of  available  heat  per  stage  will  be  proportional  to  the  squares  of 
those  ratios,  namely,  2.25  and  6.25.  Consequently  the  amounts 
of  heat  assigned  per  stage  will  be  as  follows: 

High-pressure  Intermediate         Low-pressure. 

2.2  4-95  J3-75 

If  we  decide  to  use  ten  low-pressures  and  twenty  intermediate 
stages  they  will  require 

10  X  13.75  +  20  X  4-95  =  236-5  B.T.U., 

leaving  85.5  thermal  units  which  will  require  somewhat  less 
than  39  stages.  Reversing  the  operation  it  appears  that  one 
distribution  calls  for 

10  X  13.75  +  20  X  4.95  -f  39  X  2.2  =  322  B.T.U. 

For  convenience  of  manufacture  it  is  customary  to  make 
several  stages  identical,  that  is,  with  the  same  length  of  blades, 
clearances,  etc.;  this  of  course  will  derange  the  velocities  to  some 
extent  and  interfere  with  the  realization  of  the  best  economy. 
That  part  of  the  cylinder  which  has  the  same  length  of  blades 
is  known  technically  as  a  barrel.  Let  there  be  three  barrels  for 
each  cylinder,  making  nine  in  all,  which  may  be  conveniently 
numbered,  beginning  at  the  high-pressure  end  and  may  have 


DESIGN   FOR   A   REACTION   TURBINE 


523 


the  number  of  stages  assigned  above.  In  that  table  is  given  also 
the  number  of  the  stage  counting  from  the  high-pressure  end, 
which  is  at  or  near  the  middle  of  the  length  of  the  barrel,  for 
which  calculations  will  be  made.  The  values  of  the  heat  con- 
tents ocr  +  q  are  readily  found  for  each  stage  given  in  the  table 
by  subtracting  the  amounts  of  heat  changed  into  kinetic  energy, 
down  to  that  stage,  allowing  2.2  for  each  stage  of  the  high- 

COMPOUND    REACTION   TURBINE. 


•S 

| 

i 

1 

!« 
|j 

II 

1 

>f  vaporization. 

Specific 
volume. 

1 

3 
"o 

n 

T>> 

1 

a 

3 

1 

a 

1 

1 

<J  — 

1ft 

1 

w 

1 

•| 

I 

o 

A 

£ 

§ 

£ 

£ 

M 

W 

S 

w 

0" 

3 

< 

P 

*r  +  <7 

^r+g 

<7 

r 

» 

J                 V 

I— 

i  — 

14 

7 

351 

136.3 

1177.9 

1184 

322 

869 

•  992 

3-30 

3-27 

0.415 

2  — 

13 

20 

95-4 

II49-3 

1167 

295 

890 

.980 

4.62 

4-53 

0.575 

3— 

12 

33 

298^5 

65-5 

1120.7 

1150 

268 

910 

.969 

6.60 

6.40 

0.812 

II— 

4— 

8 

43 

270 

41.8 

1087.7 

1130 

239 

93  1 

.957 

10.05 

9.62 

0.542 

5— 

6 

50 

240.5 

25-2 

1053-0 

1109 

209 

952 

•945 

16.2 

iS-3 

0.863 

6— 

6 

56 

216 

15-9 

1023.3 

1091 

184 

967 

.938 

24.9 

23.4 

1.32 

III— 

7— 

4 

61 

183 

8.02 

981.0 

1066 

151 

988 

.926 

47.1 

43-6 

0.885 

h— 

3 

65 

141 

2.96 

926.0 

1033 

109 

1013 

.912 

120 

109.5 

2.22 

9— 

3 

68 

111.5 

1-33 

884.7 

1008 

80 

1029 

•903 

255 

230 

4.67 

pressure  cylinder,  4.95  for  each  intermediate  stage  and  13.75  ^or 
each  low-pressure  stage.  For  example,  the  fiftieth  stage  has 
its  heat  contents  found  by  subtracting  from  the  initial  heat  con- 
tents 1193.3,  tne  amount 


39  X  2.2  +  ii  X  4-95  = 

leaving  for  the  heat  contents  after  that  stage  1053  thermal  units. 
The  probable  heat  contents  allowing  for  friction  and  leakage  is 
found  by  subtracting  the  product  of  the  above  quantity  by  the 
factor  0.6.  Giving 

II93.3  -   140.3   X  0.6   =  II09B.T.U. 

Having  the  values  of  x*r  +  q  obtained  in  this  way,  the  values  of 
yf  can  be  found  by  subtracting  the  heat  of  the  liquid  q,  and 


524  STEAM-TURBINES 

dividing  the  remainder  by  r.  Finally  the  specific  volumes  are 
computed  by  the  equation 

v  =  oc?u  +  T; 

but  in  practice  cr  may  be  neglected  giving 

u  =  otfs 

because  we  have  either  x  nearly  equal  to  unity  or  else  s  will  be 
larger  compared  with  <r. 

The  steam  velocity  for  the  first  cylinder  is  300  feet  per  second, 
the  weight  of  steam  per  second  is  3.15  pounds  and  the  specific 
volume  at  the  seventh  stage,  i.e.,  the  middle  of  the  first  barrel, 
is  3.27  cubic  feet.  The  effective  area  must  therefore  be 

WV   a  3. IS    X    3-27  .       , 

a  =>  144  —  ±  144  ^-^ — -° — -  =4.94  square  inches. 

To  this  must  be  added  a  fraction  of  one-third  or  one-fourth  to 
allow  for  the  thickness  of  the  blades,  and  the  result  must  be 
divided  by  sine  a  in  order  to  find  the  area  of  the  peripheral 
ring  through  which  the  steam  will  flow.  Taking  one-fourth 
for  the  fraction  in  this  case,  and  20°  for  a,  we  have 

"  -  =  1 8. i  square  inches. 

0.342  X  4 

It  is  recommended  that  the  height  of  the  blades  shall  be  0.03 
of  the  diameter,  which  gives  for  the  expression  for  the  peripheral 
ring 

0.03  nd?  =  18.1. 


.*.    d  =  ^i&.i  -r-  0.03  TT  =  13.85  inches. 

The  diameters  of  the  intermediate  and  low-pressure  cylinders 
will  be 

di  =  I3-85  X  i-5  =  20-77  in-;  d2  =  J3-85  X  2^  =  34.62  in. 
The  length  of  blade  at  the  seventh  stage  will  be 
0.03  X  13.85  =  0.415  inch. 


DESIGN    FOR   A    REACTION    TURBINE  525 

and  this  length  will  be  assigned  to  all  the  blades  of  the  first 
barrel.  The  blades  of  the  second  and  third  barrels  will  have 
their  lengths  increased  in  proportion  to  the  specific  volumes  at  the 
middle  of  those  barrels,  as  set  down  in  the  table.  The  effect 
of  increasing  the  diameters  of  the  intermediate  and  low-pres- 
sure cylinders  is  to  increase  the  steam  velocity,  and  the  peripheral 
length  of  the  steam  passage,  both  in  proportion  to  the  diameter. 
Consequently  the  lengths  of  the  blades  for  these  cylinders  are 
directly  proportional  to  the  proper  specific  volumes  and  inversely 
proportional  to  the  squares  of  the  diameters.  Thus  the  length 
of  the  blades  at  the  forty-second  stage,  i.e.,  the  middle  of  the 
fourth  barrel  is 

0.415  X  9.62  .     , 

— — =i~  =  °-542  inch. 

3.27  X  1.5 

The  lengths  are  computed  for  the  other  barrels  in  the  same  way, 
using  2.5  for  the  ratio  of  the  low-pressure  diameter. 

Since  the  diameter  of  the  small  cylinder  is  13.85  inches  and 
the  speed  of  the  vanes  on  it  is  225  feet  per  second,  the  revolutions 
per  minute  are 

225  X  60  X  12 

13-85  *~ 

Parsons  Turbine.  —  The  essential  features  of  the  Parsons 
turbine  are  shown  by  Fig.  117.  Steam  is  admitted  at  A  and 
passes  in  succession  through  the  stages  on  the  high-pressure 
cylinder,  and  thence  through  the  passage  at  E  to  the  stages  of 
the  intermediate  cylinder;  after  passing  through  the  intermediate 
stages  it  passes  through  G  to  the  low-pressure  stages  and  finally 
by  B  to  the  condenser. 

The  axial  thrust  is  counterbalanced  by  the  dummy  cylinders, 
C,  C,  C,  the  first  receiving  steam  from  the  supply  directly,  the 
second  from  the  passage  between  the  high  and  intermediate 
cylinders  through  the  pipe  F,  and  the  third  through  the  pipe  near 
G  from  the  passage  between  the  intermediate  and  low-pressure 
cylinders.  Leakage  past  the  dummy  cylinders  is  checked  by  laby- 
rinth packing,  which  is  variously  arranged  to  give  a  succession 


526 


STEAM-TURBINES 


Fro.  117. 

of  spaces  through  which  the  steam  must  pass  with  narrow  pass- 
ages,  which  throttle  the  steam  as  it  passes  from  chamber  to 
chamber.  One  method  is  to  let  narrow  strips  of  brass  into 
the  surface  of  the  cylinder  and  into  the  surface  of  the  case; 
these  strips  are  adjusted  to  leave  a  very  small  axial  clearance, 
so  that  the  steam  is  strongly  throttled  as  it  passes  through.  It 
is  reported  that  the  labyrinth  clearance  is  entirely  successful  in 
reducing  the  leakage  past  the  dummy  cylinder  to  a  small  amount. 
It  is  pointed  out  by  Mr.  Jude  that  the  most  effective  throttling 
is  at  the  last  section  of  the  labyrinth,  and  that  the  other  sections 
are  comparatively  inefficient.  This  feature  will  be  evident  if  an 
attempt  is  made  to  calculate  the  loss  by  continual  application  of 
Rankine's  equations,  page  432.  Of  course  such  a  method  can  be 
but  crude,  and  yet  its  indications  should  be  of  value  for  estimating 
leakage  which  should  be  small. 

When  applied  to  marine  propulsion  the  dummy  pistons  are 
omitted  and  the  axial  thrust  is  usefully  applied  to  the  propeller- 
shaft.  Since  an  absolute  balance  cannot  be  obtained,  a  thrust- 
bearing  is  provided  but  it  may  have  small  bearing  area  and  will 
have  but  little  friction.  Stationary  turbines  also  have  a  bearing 
for  residual  unbalanced  thrust. 

Test   on   a  Parsons  Turbine.  —  A   test   on   a   Westinghouse- 


TEST   ON   A    PARSONS   TURBINE 


527 


Parsons  turbine  in  Savannah  was  made  under  the  direction  of 
Mr.  B.  R.  T.  Collins  and  reported  by  Messrs.  H.  O.  C.  Isenberg 
and  J.  Lage,*  which  is  interesting  because  the  steam  consumption 
of  the  auxiliary  machines  was  determined  separately.  The 
data  and  results  of  tests  on  the  turbine  are  given  in  the  following 
table. 

The  tests  made  at  full  load  with  varying  degrees  of  vacuum 
show  clearly  the  advantage  obtained  in  this  machine  from  a 
good  vacuum,  which  amounted  to  a  saving  of 


289  —  279 
289 


0.035, 


TESTS   ON  WESTINGHOUSE-PARSONS   TURBINE. 
COLLINS,  ISENBERG  AND  LAGE. 


i  load. 

|  load. 

] 

?ull  load. 

ii  load. 

i*  load. 

Duration  minutes   

60 

60 

60 

60 

60 

45 

45 

Steam  pressures,  gauge  .    .    . 

I3i 

129 

128 

127 

128 

127 

I25 

Vacuum  inches            .... 

28.1 

28.1 

2<    7 

26   7 

28.0 

26    7 

26.6 

Revolutions  per  minute      .    . 

3616 

3601 

3  •  1 
3602 

/ 
3612 

35°2 

^\j  .  f 
3540 

3537 

Load  kilowatts    

260 

370 

40  2 

^OI 

4.QQ 

629 

733 

Steam  consumption,   pounds 

o  i  y 

tyo 

0WA 

tyy 

1  66 

per  kilowatt-hour    .... 

24-3 

21.2 

20.7 

19.8 

19.7 

19.8 

20.2 

per  electric  h.p.  per  hour  . 

18.1 

15-8 

15-6 

14.8 

14.7 

14.7 

I5-I 

Heat  consumption  B.T.U. 

per  kilowatt-minute 

462 

403 

494 

375 

374 

373 

38l 

per  horse-power  per  minute 

345 

301 

289 

284 

279 

278 

283 

A  great  importance  is  attributed  by  turbine  builders  to  obtaining 
a  low  vacuum,  in  many  cases  special  air-pumps  and  other  devices 
being  used  for  that  purpose.  Unless  discretion  is  shown  both 
in  the  design  and  operation  of  this  auxiliary  machinery,  its  size 
and  steam  consumption  is  likely  to  be  excessive,  and  what  appears 
to  be  gained  from  the  vacuum  may  be  entirely  illusory. 


*  Thesis,  M.I.T.  1906. 


528  STEAM-TU  RBINES 

The  steam  consumption  in  pounds  per  hour  for  the  several 
auxiliary  machines  was  as  follows: 

Centrifugal  pump  for  circulating  water .     .     .     .     88 1 

Dry  vacuum  pump 212 

Hot-well  pump 42.8 

H35-8 

This  total  was  equivalent  to  0.115  of  the  steam  consumption 
of  the  turbine  at  full  load  and  with  28  inches  vacuum.  Some 
tests  of  turbine  installations  show  twice  or  three  times  this 
proportion. 

Effect  of  Friction  on  Entropy.  —  Attention  has  been  called  to 
the  fact  that  the  effect  of  friction  is  to  increase  the  entropy  of 
steam,  and  that  in  consequence  any  method  of  designing  com- 
pound turbines  which  depends  on  determination  of  intermediate 
temperatures  and  pressures  at  the  initial  entropy  is  liable  to  appre- 
ciable error. 

In  the  discussion  of  the  problem  on  page  506  for  a  two-stage 
turbine,  the  total  available  adiabatic  heat  is  found  to  be  322  B.T.U., 
which  being  divided  into  equal  parts  assigns  161  units  per  stage. 
The  intermediate  temperature  is  found  to  be  223°,  corresponding 
to  1 8. 2  pounds  absolute.  But  the  effect  of  internal  steam  friction 
and  other  conditions  is  to  reduce  the  heat  actually  changed  into 
work  to 

0.883  X  0-85  X  0.75  X  161  =  0.563  X  161  =  90.6  B.T.U. 

The  entropy  is  thus  increased  to   1.66  at  which  the  adiabatic 
heat  for  the  second  stage  is  found  to  be 

1 100  —  927  =  173  B.T.U. 

In  consequence  the  velocity  of  steam  from  the  second  set  of 
nozzles  is  computed  to  be  2710  feet  per  second  instead  of  2610, 
as  previously  calculated. 

It  is  evident  that  the  intermediate  temperature  and  pressure 
must  be  reduced  if  the  two  stages  are  to  have  the  same  peripheral 
velocity.  A  crude  way  of  doing  this  would  be  to  take  the  mean 


EFFECT    OF   FRICTION   ON    ENTROPY  529 

of  161  and  173,  namely,  167  units  for  determining  the  intermedi- 
ate temperature.  The  heat  contents  then  become 

1193  —  167  =  1026, 

which  at  1.56  entropy  corresponds  to  2 19°. 5  or  17  pounds.  A 
step-by-step  process  will  now  show  less  discrepancy,  and  a  third 
computation  would  be  satisfactory;  but  such  a  cut-and-try 
method  becomes  very  tedious  when  there  are  a  large  number  of 
stages.  By  the  aid  of  the  entropy  table  it  is  possible  to  make  a 
direct  determination  of  the  proper  intermediate  temperatures, 
which  shall  give  concordant  results  from  the  step-by-step  calcu- 
lation. 

Internal  Heat  Factor.  —  In  the  preliminary  computation,  on 
page  506,  three  factors  were  assigned,  one  (0.85)  to  allow  for  the 
friction  in  the  nozzle,  another  (0.883)  to  ta^e  account  of  the 
angles  of  guides  and  blades,  and  a  third  (0.75)  to  take  account  of 
steam  friction.  A  more  precise  analysis  of  the  action  of  the 
steam  shows  that  the  latter  two  cannot  be  separated  as  in  the 
preliminary  calculation,  but  the  general  conception  is  sufficient 
for  its  use  in  that  place.  The  product  of  these  three  factors, 

0.85  X  0.883  X  0.75  =  0.563, 

may  be  called  the  internal  heat  factor.  It  is  also  the  ratio  of  the 
steam  per  horse-power  per  hour  computed  by  Rankine's  cycle,  to 
the  actual  steam  per  turbine  horse-power  per  hour;  the  latter 
corresponding  roughly  to  the  steam  per  indicated  horse-power  per 
hour  for  a  reciprocating  engine,  which  is  the  proper  basis  for  heat 
comparisons.  In  the  discussion  on  page  507,  the  factor  0.9  is 
used  to  allow  for  mechanical  efficiency,  leading  to  the  determina- 
tion of  15.7  as  the  steam  per  brake  horse-power  per  hour,  to  which 
some  addition  is  suggested  for  leakage  and  radiation. 

Starting  with  the  actual  steam-consumption  per  brake  horse- 
power as  determined  by  a  test  on  a  turbine  already  installed,  we 
may  allow  for  radiation  and  gland  leakage  and  for  mechanical 
efficiency  and  so  estimate  the  steam  per  turbine  horse-power  per 
hour.  It  will  appear  that  considerable  uncertainty  in  the  factors 
assigned  for  this  purpose  will  have  but  little  effect  on  the  deter- 


53° 


STEAM-TU  RBINES 


mination  of  pressures.  If  it  be  assumed  that  such  a  test  shows 
that  16.5  pounds  of  steam  are  required  per  turbine  horse-power 
per  hour,  and  if  we  assign  0.95  to  allow  for  radiation  and  gland 
leakage  and  0.9  for  the  mechanical  efficiency  we  shall  have 

16.5  X  0.95  X  0.9  =  14.1 

for  the  turbine  steam  consumption.  The  thermal  units  per 
horse-power  per  minute  for  Rankine's  cycle  were  found  to  be 
149;  which  corresponds  to 

149  X  60  -T-  1123  =  7.96 
and  7.96  -T-  14.1  =  .564 

which  corresponds  sufficiently  with  the  value  previously  assigned. 

Having  the  value  assigned  to  the  internal  heat  factor  we  may 
determine  that  of  the  available  adiabatic  heat  only 

322  X  0.563  =  181.4 

will  finally  be  changed  into  work  per  pound  of  steam.  And  if 
this  be  equally  divided  between  two  stages  the  heat  yielded  in 
each  stage  per  pound  of  steam  will  be 

181.4  -T-  2  =  90.7 

thermal  units.  The  amount  of  heat  changed  into  work  per  pound 
of  steam  being  based  on  the  actual  steam  consumption  of  the 
turbine,  when  once  assigned  by  aid  of  the  proper  factors,  must 
be  accepted  for  all  consequent  computations. 

Method  for  Determining  Intermediate  Pressures.  —  This 
method  for  determining  the  intermediate  temperatures  and  corres- 
ponding pressures  for  a  turbine  with  several  pressure  stages  is  to  be 
justified  by  its  convenience  and  concordance  with  a  step-by-step 
calculation.  It  can  be  stated  best  by  aid  of  an  example.  The 
same  pressure  will  be  chosen  as  on  page  506,  but  the  computation 
will  be  carried  to  the  degree  of  precision  possible  with  the  entropy 
table,  as  is  necessary  for  the  best  results.  At  1.56  entropy,  and  at 


METHOD  FOR  DETERMINING  INTERMEDIATE  PRESSURES      531 


temperatures  366°  and  102°  the  heat  contents  and  their  difference 
are 

1193.3  ~  871-1  =  322-2. 

Let  this  total  available  heat  be  divided  into  four  equal  parts 
which  will  give  three  intermediate  temperatures,  or  five  tempera- 
tures in  all,  as  shown  in  the  following  table: 


Heat  contents, 
entropy  1.56.  . 

Temperature. 

Heat 
contents. 

Differences. 

"93-3 
80.6 

1112.7 

80.6 
1032.1 

80.6 
951-5 

80.6 

870.9 

366 

-•IS 

H™ 

1124.4 
uoi.8 

22.6 

24.5 

26.5 

28.5 

1043  .  8 
1019.3 

964.2 
937-7 

885.4 
856.9 

At  each  temperature,  except  the  first,  the  variation  of  heat  con- 
tents for  twenty  degrees  is  determined;  for  example,  at  302°  the 
heat  contents  is  1124.4  and  at  282°  it  is  1 101.8,  giving  a  differ- 
ence of  22.6  B.T.U. 

The  next  step  is  to  find  the  entropy  of  the  steam  at  the  several 
temperatures  with  an  internal  heat  factor  which  can  be  taken  as 
0.563  for  a  convenient  mean  value. 

For  this  purpose  the  amount 

80.6  X  0.563  =  45.4 

is  subtracted  four  times  successively,  and  the  nearest  entropy  col- 
umn is  sought  in  the  entropy  table.  The  variation  is  determined 
again  in  the  entropy  column. 


532 


STEAM-TURBINES 


Temper- 
ature. 

Heat 
contents. 

Nearest 
entropy. 

Heat 
contents. 

Differences. 

366 

II93-3 

1.56 

.  .  . 

. 

45-4 

292 

II47-9 
45-4 

'•*|s 

1162.5 
1138.8 

23-7 

223 

1102.5 

i.66J^3 

1113.1 
1086.5 

45-4 

26.6 

160 

1057.1 
45-4 

'•"{III 

1071.2 
1041.3 

29.9 

(   112 

1028.2 

102 

ion  .7 

r'8li      92 

994-7 

33-5 

The  differences  in  this  last  table  are  divided  by  those  in  the 
preceding  table,  and  the  ratios  are  set  down  in  the  following 
table.  The  computation  for  the  first  step  is  omitted,  as  it  would 
evidently  give  unity  for  the  ratio. 


Ratio  of 
differences. 

Mean  value. 

Factor. 

i.oooX 
1.049 
i.  086 
1.128 
I.I7SX 

|=0.500 
1.049 
1.  086 
1.128 
l=o.587 

1.087 
1  .000 
0.913 

4/4  •  35Q 
1.087 

The  mean  value  of  the  ratio  is  now  to  be  obtained  by  taking 
the  sum  of  half  of  the  extreme  values  and  all  the  other  values  and 
dividing  by  four.  The  factors  in  the  last  column  are  the  mean 
value  thus  obtained,  unity  and 

i  —  0.087. 


The  direct  solution  for  intermediate  temperature  and  pressure 
can  now  be  made  by  aid  of  Fig.  118,  in  which  hfa  represents  the 


METHOD  FOR  DETERMINING  INTERMEDIATE  PRESSURES      533 


At  \  is   laid   off  the   abscissa 
as   the  base  unity,  and  the 


, 


FIG.  118. 


total   available   adiabatic   heat. 

1.087,  and  at  hv  0.913  from   \\ 

diagonal  line  is  drawn   as  shown. 

Now  divide  the  line  hji2  into  por- 

tions   representing    the    heat    that 

would  be  assigned  to  each  of  the 

stages  of  a  turbine  having  adiabatic 

action.     In  this  case,  since  the  tur- 

bine has  the  same  pitch   diameter 

for  the  two  stages  and  since,  conse- 

quently, the  steam  velocity  at  dis- 

charge from  the  nozzles  must  be  the  same,  the  line  hfy  may  be 

bisected  at  o.     When  the  pitch  diameters  are  unequal  the  heat 

assignments  would  be  unequal,  and  the  line  hji2  would  be  divided 

unequally.     At  the  midpoints  of  the  sections  abscissae  are  drawn 

and  measured;  they  give  in  the  figure  the  factors  1.043  and  °-957- 

The  total  available  adiabatic  heat,  322.2  units,  is  now  divided  into 

equal  parts,  giving  161.1  for  each.     These  parts  are  now  to  be 

multiplied  by  the  factors  just  obtained  giving 

First  stage        161.1  X  1.043  =  168.0 

Second  stage    161.1  X  0.957  =  154.2 


322.2 
The  intermediate  temperatures  are  found  as  follows 


Heat  contents, 
entropy  1.56. 

Temperature. 

Pressure. 

H93-3 

1  68.0 

366 
218 

164.8 
16.5 

1025.3 
154.2 

871.1 

102 

I  .0 

Making  a  calculation  like  that  on  page  512  we  have  for  the 
heat  applied  to  driving  the  turbine  in   each  stage   90.7  thermal 

units. 


534 


STEAM-TURBINES 


The  heat  contents  of  the  steam  approaching  the  second  set  of 
nozzles  is 

1193.3  ~  9°-7  =  1 102.6. 

This  is  found  most  nearly  at  entropy  1.67  for  the  temperature 
218°.     The  available  heat  for  adiabatic  action  is 

Temperature   218°       Heat  contents 
102° 

167.0 

The  difference  between  this  figure  and  that  assigned  at 
entropy  1.56  to  the  first  stage  is  0.6  per  cent.  The  probable  error 
of  this  method,  depending  as  it  does  on  the  precision  of  the  entropy 
table,  is  about  the  same  under  all  conditions.  The  percentage  of 
error  is,  therefore,  larger  when  there  are  many  stages.  But  for 
turbine  having  many  stages  the  computations  are  conveniently 
made  at  intervals  so  that  the  error  need  never  be  important. 

Variation  of  Ratios.  —  To  show  the  effect  of  varying  the  heat 
factor  for  internal  operations  the  following  table  has  been  com- 
puted. 

(Ratios  to  allow  for  influence  of  increase  of  entropy,  due  to  steam 
friction.  One  hundred  and  fifty  gauge  pressure  to  28  inches 
vacuum.) 

Heat  factor 0.55  0.60  0.65  0.70  0.75 

Ratios,  initial 1.090  1.078  1.065  I-°S^>  I-°5° 

Midpoint i.ooo  i.ooo  i.ooo  i.ooo  i.ooo 

Final 0.910  0.922  0.935  0.942  0.950 

This  table  shows  that  probable  variations  in  the  heat  factor 
have  little  effect  on  the  determination  of  intermediate  tempera- 
tures and  pressures.  The  same  fact  is  brought  out  in  the  follow- 
ing statement  of  the  intermediate  temperature  for  the  two-stage 
turbine,  discussed  in  the  preceding  section. 

Heat  factor 0.55         0.65         0.75 

Intermediate  temperature 218  219  220 

Pressure 16.5         16.9         17.2 


APPLICATION  TO   SIX-STAGE  TURBINE 


535 


Application  to  Six-stage  Turbine.  —  To  further  illustrate  the 
method  of  determining  temperatures  the  following  application  is 
made  to  a  turbine  with  six  equal  stages. 
The  factors  are  determined  by  aid  of  Fig. 
119  for  a  heat  factor  0.65.  The  total 
available  heat  is  divided  into  six  parts, 
using,  as  before,  150  pounds  gauge 
pressure  and  a  vacuum  of  28  inches. 
The  mean  assignment  per  stage  is  there- 
fore 
FIG.  119.  (ii93-3  -  871.1)  -5-6=  53.7. 

The  heat  assignments  at  entropy  1.56  are 
53.7  X  1.054  =  56.6 
53.7  X  1.032  =  55.4 
53.7  X  i.on  =  54.3 
53.7  X  0.989  =  53.1  J 
53.7  X  0.968  =  52.0 
53.7  X  0.946  =  50.8 

The  computation   of  the   intermediate   temperatures   and   the 
check  computation  are  given  in  the  following  table: 


Heat 
contents, 
entropy  1.56 

Temper- 
atures. 

Pres- 
sures. 

Heat 
contents, 
factor  0.65. 

Entropy. 

Heat 
drop. 

"93-3 
56.6 

1136.7 
53-4 

1081.3 
54-3 

1027.0 
53-i 

973-9 
52.0 

921.9 
50.8 

871.1 

366.0 
3I3-0 
264.3 
219.3 
177-4 
138.3 
102.0 

164.8 
80.  I 

38-1 
16.9 
7.09 
2.76 
I.OO 

"93-3 
34-9 

1158.4 
34-9 

"23.5 
34-9 

1088.  6 
34-9 

1088.7 
34-9 

1053-8 
34-9 

983-9 

1.560 
1.588 
1.618 
1-651 
1.685 
1.722 
1.761 

U93-3 
1136.7 
ef\    f\ 

5O.O 
H58.4 

noi  .5 

"  5^-9 
ii23-5 
1066.4 

1088.  6 
1031.9 

5°-7 
1053-7 
996.7 

57-o 
1018.8 
962.1 

-A      .. 

5°-7 

536  STEAM-TURBINES 

In  the  check  calculation  the  heat  changed  into  work  per  stage 

is  taken  to  be 

53.7  X  0.65  =  34.9. 

This  quantity  subtracted,  successively  gives  the  heat  contents  of 
the  steam  approaching  the  several  sets  of  nozzles.  The  cor- 
responding entropies  are  found  by  interpolation  in  the  entropy 
table.  At  these  entropies  the  heat  contents  are  found  for  the 
initial  and  final  temperatures  for  the  several  stages;  the  differences 
are  the  available  heats  for  adiabatic  action  in  these  stages.  The 
variation  of  the  heat  drops  from  the  assigned  value  56.6  is  a 
measure  of  the  precision  of  the  method. 

In  this  sample  computation  the  work  is  carried  to  the  limit  of 
precision  of  the  entropy  table.  Usually  it  will  be  sufficient  to 
take  the  nearest  temperature  from  that  table  and  to  make  the 
check  computation  in  the  nearest  entropy  column,  thus  avoiding 
the  labor  of  interpolating,  which  is  considerable  when  cross-inter- 
polation is  undertaken.  Occasionally  it  may  be  worth  while  to 
work  to  half  degrees  of  temperature. 

The  discussion  of  the  properties  of  steam  in  Chapter  VI 
shows  that  our  knowledge  is  not  more  precise  than  is  represented 
by  a  single  thermal  unit;  it  is  convenient  to  have  tenths  of  units 
in  our  steam  tables,  and  such  a  degree  of  precision  is  required  in 
order  to  use  the  method  explained  for  determining  intermediate 
temperatures  for  compound  turbines.  The  method  can  be  de- 
pended on  to  give  concordant  results,  and  the  check  calculation 
is  valuable  mainly,  as  it  gives  a  good  arithmetical  check  on  the 
calculation. 

Unequal  Stages.  —  In  the  examples  given  of  the  method  of 
determining  intermediate  temperatures,  the  several  stages  have 
been  assigned  equal  amounts  of  heat.  If  the  amounts  of  heat 
assigned  are  unequal,  the  line  /^2,  of  Fig.  118,  is  to  be  divided 
correspondingly,  and  the  abscissae  are  to  be  drawn  at  the  mid- 
points to  determine  the  ratios.  The  check  calculation  is  to  be 
carried  out  with  the  true  amount  of  heat  changed  into  work  for 
each  stage,  obtained  by  multiplying  the  adiabatic  assignment  by 
the  heat  factor. 


HEAT   FACTORS;    OVERALL,    AND   PER    STAGE  537 

Heat  Factors ;  Overall,  and  per  Stage.  —  The  heat  factors 
used  in  the  method  for  determining  the  pressures  and  temperatures 
for  a  turbine  are  made  to  depend  on  the  comparison  of  the  steam 
per  horse-power  per  hour  for  Rankine's  cycle  and  the  steam  per 
turbine  horse-power.  This  may  be  called  the  overall  heat  factor. 
Though  its  precise  determination  may  be  difficult  it  has  been 
shown  that  a  fair  approximation  is  all  that  is  required  for  deter- 
mining pressures. 

When  we  come  to  analyzing  the  heat  losses  in  a  stage  of  a  tur- 
bine another  heat  factor  is  required.  This  is  evident  from  the 
consideration  that  on  page  533  the  heat  assigned  to  each  stage  of 
a  two-stage  turbine  is  168  thermal  units;  while  the  heat  changed 
into  work  is  only  90.7  units.  This  gives  a  ratio 

90.7  -v-  168  =  0.540 

instead  of  0.563,  which  was  taken  for  the  overall  factor.     The 
factor  can  be  obtained  also  as  follows : 

0.563  -5-  1.043  =  °-540- 

This  factor  can  be  taken  to  be  the  product  of  factors  (i)  for 
the  nozzle,  (2)  for  the  action  of  the  blades  and  girders,  and  (3) 
for  the  steam  friction  on  the  disk,  and  other  similar  effects.  If  a 
factor  0.85  be  assigned  to  the  nozzle,  a  factor  0.75  to  the  wheels, 
etc.,  and  a  factor  0.75  to  the  friction  of  the  disk  and  similar 
actions,  the  product  becomes 

0.85  X  0.75  X  0.85  =  0.542. 

An  intelligent  discussion  of  these  matters  can  be  had  only  with 
special  data  from  experiments  on  turbines  and  on  single  stages  of 
turbines. 


INDEX. 


Absolute  temperature 

Absorption  refrigerating  apparatus 
Adiabatic  for  gases 

for  liquid  and  vapor 

lines 

Adiabatics,  spacing  of 

After  burning 

Air-compressor,  calculation  .  .  . 

compound 

cooling  during  compression   .    . 

effect  of  clearance 

efficiency 

friction 

fluid  piston 

moisture  in  cylinder 

power  expended 

three-stage 

Air,  flow  of 

friction  in  pipes 

pump 374, 

thermometer 

Alternative  method 

Ammonia 

Automatic  and  throttle  engines  . 

Bell-Coleman     refrigerating     ma- 
chine       

Binary  engines 180, 

Blast-furnace  gas-engine    .    ,    .    . 

Boyle's  law 

British  thermal  unit 

Biichner 


Calorimeter 

separating 

Thomas 

throttling 

Calorie 

Callendar  and  Nicolson 


56 
411 

63 
100 

17 


377 
366 
360 
363 
370 
369 
359 
361 
362 
368 

429 
380 

375 
368 

49 
123 
276 


413 
280 

335 

54 

5 

437 

191 
194 

'95 
161 

5 

231 


Carnot's  engine 

function 

principle 

Characteristic  equation  .... 

for  gases 

for  superheated  vapors  .  .  . 
Chestnut  Hill,  engine  test  .  .  . 
Compound  air-compressor  .  . 

air-engine 

Compound-engines  ...... 

cross-compound 

direct-expansion 

indicator  diagrams 

low-pressure  cut-off     .... 

ratio  of  cylinders 

total  expansions 

with  receiver 

without  receiver  ...... 

Compressed-air 

calculation 

compound  compressor    .    .    . 

effect  of  clearance 

friction,  etc 

hydraulic  compressor      .    .    . 

interchange  of  heat     .... 

storage  of  power 

temperature  after  compression 

transmission  of  power  .  .  . 
Compressed-air  engine  .... 

calculation 

compound 

consumption 

final  temperature 

interchange  of  heat 

moisture  in  cylinder    .... 

volume  of  cylinder 

Condensers 

cooling  surface 

ejector  


PAGE 

22 

28 

26 

2 

55 
no 

239 
366 

384 
156 
169 

163 
162 
161 
162 
1 60 
J59 
158 
358 
377 
366 

363 
369 
372 
365 
392 
364 
39i 
384 
388 
388 
385 
385 
386 
30i 

386 
149 
151 

471 


539 


540 


INDEX 


PAGE 

Carburetors      334 

Creusot,  tests  on  engine     ....  248 

Critical  temperature 71 

Cut-off  and  expansion    .....  273 

Cycle,  closed 25 

non-reversible 40 

reversible 24 

Delafond 248 

Denton      419,20 

Density  at  high-pressure    ....  71 

Dryness-f  actor 86 

Designing  steam-engines    .    .     152,  179 

Diesel  motor 341 

economy 355 

Differential  coefficient  dp/dt      .    .  79 

DixwelFs  tests 270 

Dynamometers 186 

Economy,  methods  of  improving.  245 

compounding 257 

expansion 256 

increase  of  size 255 

intermediate  reheaters  ....  268 

of  steam-engines 237 

raising  pressure 247 

steam-jackets 261,  266 

superheating 270 

variation  of  load  274 

Effectof  raising  steam  -pressure,  148,  247 

Efficiency  25 

mechanical 287 

of  reversible  engines 33 

of  steam-engine 130,  144 

Efficiency,  maximum  39 

of  superheated  steam  ....  115 

Ejector 470 

condenser 471 

Engine,  Carnot's 22 

compressed-air 384 

friction  of  •  .' 285 

hot-air 298 

internal  combustion 298 

oU  .  .  . 335 

reversible 24 

Entropy 32 


Entropy  —  Continued. 

due  to  vaporization     .... 

expression  for 

of  a  liquid 

of  a  liquid  and  vapor      .    .    . 

of  gases     

scale  of 

Exponential  equation      .... 

First  and  second  laws  combined 
First  law  of  thermodynamics     . 

application  of 

application  of  vapors  .... 
Flow  in  tubes  and  nozzles  .  . 

Biichner's  experiments   .    .    . 

design  of  a  nozzle 

experiments      

friction  head 

Kneass'  experiments   .... 

Kuhhardt's  experiments     .    . 

Lewicki's  experiments    .    .    . 

Rateau's  experiments      .    .    . 

Rosenhain's  experiments    .    . 

Stodola's  experiments  .  .  . 
Flow  of  air,  Fliegner's  equations 

in  pipes 

maximum  velocity 

through  porous  plug  .... 
Flow  of  fluids 

of  gases     

of  incompressible  fluids      .    . 

of  saturated  vapor 

of  superheated  steam  .  .  . 
French  and  English  units  .  .  . 
Friction  of  engines 

distribution 

initial  and  load    . 


99 
35 
97 
99 
67 

3i 
66 

49 
13 

45 
87 
434 
437 
444 
436 
435 
440 

443 
442 
440 
441 
441 
429 
380 

43° 
69 

423 
426 

425 
430 
433 
56 
285 

295 
287 


Gas-engine 304 

after  burning 319 

blast-furnace  gas 333 

economy  and  efficiency  .    .     320,  348 

ignition 329 

starting  devices 329 

temperature  after  explosion  .    .  318 

valve-gear 324 

water  jackets 320 


INDEX 


541 


Gas-engines  —  Continued. 

with  compression  in  cylinder     .  308 

with  separate  compression     .    .  305 

Gas-engines  four-cycle  .....  337 

two-cycle 338 

Gases 54 

adiabatic  equations 64 

characteristic  equation   ....  55 

characteristics  for  gas-engines  .  314 

entropy 67 

general  equations 61 

intrinsic  energy 66 

isoenergic  equation 63 

isothermal  equation 61 

special  method 60 

specific  heats 59 

specific  volumes 57 

Gasoline  engine 334 

Gas-producers 33*>352 

Gauges      186 

Gay-Lussac's  law 54 

Graphical  representation  of  change 

of  energy 20 

of  characteristic  equation  ...  4 

of  efficiency 33 

GrashofPs  formula      432 

Hall's  investigations 230 

Hallauer's  tests 219 

Heat  of  the  liquid 81 

Heat  of  vaporization 81 

Hirn  engine,  tests  on 220 

Hirn's  analysis 205 

Hot-air  engines 298 


Ignition 

Indicators .  . 

Influence  of  cylinder  walls 

Callendar  and  Nicolson 

Hall  . 


•  329 

.  187 

•  199 

•  231 
.  230 

Hirn's  analysis 205 

representation 202 

Injector 447 

combining-tube 458 

delivery-tube 459 

double 461 


Injector  —  Continued. 

efficiency  of 459 

exhaust  steam 467 

Korting 462 

lifting 460 

restarting 464 

self-adjusting 462 

Seller's      460 

steam-nozzle 458 

theory 448 

velocity  in  delivery  tube    ...  455 

velocity  of  steam -jet 452 

velocity  of  water      454 

Internal  combustion  engines      .    .  298 

Internal  latent  heat 86 

Intrinsic  energy 14 

of  gases 66 

of  vapors 95 

Isoenergic  or  isodynamic  line    .    .  17 

for  gases 63 

Isothermal  lines 16 

for  gases 61 

for  vapors 94a 

Josse,  tests  on  binary  engine  .    .  282 

Joule  and  Kelvin's  experiments    .  69 

Kelvin's  graphical  method     ...  29 

Kerosene-oil  engine 335 

Kilogram 56 

Kneass 440-452 

Knoblauch no 

Kuhhardt 443 

Latent  heat  of  expansion   ....  6 
Laws  of  thermodynamics  .    .    .     13,  22 

application  to  gases 59 

application  to  vapors 88 

Lewicki 442 

Lines,  adiabatic 17 

isoenergic      .........  17 

isothermal     . 16 

of  equal  pressure 16 

of  equal  volume  .......  16 

Meyer 350 

Mass.    Inst.    Technology,    engine 

tests  ....  262 


542 


INDEX 


Mechanical  efficiency 286 

Mechanical  equivalent  of  heat  .    .       78 
Meter 56 


Non-reversible  cycles 


40 


Oil-engine  economy 355 

Oil-engines 335 

Porous  plug,  flow  through     ...  69 

Pressure  of  saturated  steam  ...  83 

of  vapors 84 

specific 2 


Quality      .    .    .    . 


86 


Rankine's   equations   for   flow  of 

steam 432 

cycle 134 

Rateau 440 

Ratio  of  cylinders,  compound  en- 
gines       162 

Refrigerating  machines 396 

absorption 411 

air      396 

calculations  for 403,  408 

compression 405 

fluids,  for 409 

proportions 398,  406 

tests 412,  413,  417 

vacuum 398 

Regnault's  equations  for  steam     .       77 

Relations  of  thermal  capacities     .       12 

of  adiabatics  and  isothermal  lines    18 

Reversible  cycle 24 

engine 24 

Rontgen's  experiments 72 

Rosenhain 441 

Rowland 81 

Saturated  vapors       76 

adiabatic  equations 100 

entropy 97>  99 

flow  of 430 

general  equation      87 

intrinsic  energy 95 

isoenergic  equation 95 

isothermal  equation 94 


Saturated  vapors  —  Continued. 

pressure  of 77 

specific  heats 93 

specific  volumes 91 

Saturated  vapors,  special  method.       90 
Schroter's    tests    of    refrigerating 

machines 412,  417 

tests  of  steam-engines     ....     273 
Seaton's    multipliers    for    steam- 
engine  design 179 

Second  law  of  thermodynamics      22,  27 

application  of 47 

application  to  vapors 88 

Specific -heat 6,  58 

of  gases 58 

of  liquids 83 

of  superheated  steam      ....       93 

of  water 78 

Specific-heats,  ratio  of 59 

Specific-pressure      56,  82 

Specific-volume 3 

of  gases 57 

of  liquids 84 

of  vapors 88,  90 

Starting  devices 325 

Steam-engine 128 

actual 142 

Carnot's  cycle 128 

compound 156 

designing 152,  179 

economy 245 

efficiency 130 

Hirn's  analysis 205 

indicators 187 

influence  of  the  cylinder  walls  .     199 

leakage  of  valves 234 

variation  of  load      274 

Seaton's  multipliers     .....     179 

triple-expansion 172 

with  non-conducting  cylinder    .     134 

Steam  turbines      472 

compound        4^6 

compounding  velocity     ....     487 

"  pressure       ....     493 

pressure  and  velocity  506 


INDEX 


543 


Steam  turbines  —  Continued. 

Curtis 513 

effect  of  friction 481,  491 

impulse 473 

"       general  care 477 

internal  heat  factor 529 

friction  of  rotating  disks    .    .    .  504 

lead 502 

leakage  and  radiation     ....  501 

noaxial  thrust 480 

Rateau 503 

reaction 476,  515,  520 

temperature  distribution    .    .    .  530 

Stirling's  hot-air  engine     ....  299 

Stodola 441 

Sulphur  dioxide 117 

Superheated  vapors no 

characteristic  equation  ....  121 

entropy 115 

specific-heat 112 

total  heat      114 

Temperature 3 

absolute  scale 29 

standard 5,  81 

Temperature-entropy  diagram 

35,  104,  131,  137 

table      106,  139 


Testing  steam-engines 183 

Tests  of  steam-engines 237 

examples  of  economy 238 

marine  engines    ....         241,  242 

simple  engines 250 

steam-pumps        244 

superheated  steam  ....     270,  273 

Thermal  capacities 1,7 

of  gases 61 

relations  of       9 

Thermal  lines 16 

and  their  projections 19 

Thermal  unit       5 

Thomas 112 

Thurston 294 

Total  heat  of  steam 81 

of  superheated  steam     ....  114 

of  vapors 85 

Triple-expansion  engines       ...  172 

Tumlirz in 

Value  of  R 57 

Waste-heat  engine 357 

Weirs 191 

Zeuner's  equations          51 


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Black's  United  States  Public  Works Oblong  4to,  5  00 

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Burr's  Elasticity  and  Resistance  of  the  Materials  of  Engineering 8vo,  7  50 

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Fowler's  Ordinary  Foundations 8vo,  3  50 

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11 


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12 


MECHANICAL   ENGINEERING. 

MATERIALS    OF    ENGINEERING,  STEAM-ENGINES   AND    BOILERS. 

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Jamison's  Advanced  Mechanical  Drawing 8vo,  2  00 

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Jones's  Gas  Engine 8vo,  4  00 

Machine  Design; 

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Leonard's  Machine  Shop  Tools  and  Methods 8vo,  4  00 

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Mechanical  Drawing 4to,  4  00 

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Mehrtens's  Gas  Engine  Theory  and  Design Large  12mo,  2  50 

Oberg's  Handbook  of  Small  Tools Large  12mo,  3  00 

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Peele's  Compressed  Air  Plant  for  Mines 8vo,  3  00 

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Reid's  Course  in  Mechanical  Drawing 8vo,  2  00 

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Richards's  Compressed  Air 12mo,  1   50 

Robinson's  Principles  of  Mechanism 8vo,  3  00 

Schwamb  and  Merrill's  Elements  of  Mechanism 8vo,  3  00 

Smith  (A.  W.)  and  Marx's  Machine  Design 8vo,  3  00 

Smith's  (O.)  Press-working  of  Metals 8vo,  3  00 

Sorel's  Carbureting  and  Combustion  in  Alcohol  Engines.      (Woodward  and 

Preston.) Large  12mo,  3  00 

Stone's  Practical  Testing  of  Gas  and  Gas  Meters 8vo,  3  50 

13 


Thurston's  Animal  as  a  Machine  and  Prime  Motor,  and  the  Laws  of  Energetics. 

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Treatise  on  Friction  and  Lost  Work  in  Machinery  and  Mill  Work.  .  .8vo,  3  00 

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Wood's  Turbines 8vo,  2  50 


MATERIALS    OF   ENGINEERING. 

*  Bovey's  Strength  of  Materials  and  Theory  of  Structures 8vo,  7  50 

Burr's  Elasticity  and  Resistance  of  the  Materials  of  Engineering 8vo,  7  50 

Church's  Mechanics  of  Engineering 8vo,  6  00 

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Steels,  Steel-Making  Alloys  and  Graphite Large  12mo,  3  00 

Johnson's  (J.  B.)  Materials  of  Construction 8vo,  6  00 

Keep's  Cast  Iron 8vo,  2  50 

Lanza's  Applied  Mechanics 8vo,  7  50 

Maire's  Modern  Pigments  and  their  Vehicles 12mo,  2  00 

Martens's  Handbook  on  Testing  Materials.      (Henning.) 8vo,  7  50 

Maurer's  Techincal  Mechanics 8vo,  4  00 

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Metcalf's  Steel.     A  Manual  for  Steel-users 12mo,  2  00 

Sabin's  Industrial  and  Artistic  Technology  of  Paint  and  Varnish 8vo,  3  00 

Smith's  ((A.  W.)  Materials  of  Machines .". 12mo,  1  00 

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Constituents 8vo,  2  50 

Wood's  (De  V.)  Elements  of  Analytical  Mechanics 8vo,  3  00 

Treatise  on    the    Resistance    of    Materials    and    an    Appendix    on    the 

Preservation  of  Timber 8vo,  2  00 

Wood's  (M.  P.)  Rustless  Coatings'    Corrosion  and  Electrolysis  of  Iron  and 

Steel 8vo,  4  00 


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Carnot's  Reflections  on  the  Motive  Power  of  Heat.      (Thurston.) 12mo,  1   50 

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Goss's  Locomotive  Performance 8vo,  5  00 

Hemenway's  Indicator  Practice  and  Steam-engine  Economy 12mo,  2  00 

Hutton's  Heat  and  Heat-engines 8vo,  5  00 

Mechanical  Engineering  of  Power  Plants 8vo,  5  00 

Kent's  Steam  boiler  Economy 8vo,  4  00 

14 


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Smart's  Handbook  of  Engineering  Laboratory  Practice 12mo,  2  50 

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Spangler's  Notes  on  Thermodynamics 12mo,  1   00 

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Thurston's  Handbook  of  Engine  and  Boiler  Trials,  and  the  Use  of  the  Indi- 
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Handy  Tables 8vo,  1  50 

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Wehrenfennig's    Analysis  and  Softening  of  Boiler  Feed-water.     (Patterson). 

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MECHANICS    PURE   AND    APPLIED. 

Church's  Mechanics  of  Engineering 8vo,  6  00 

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Dana's  Text-book  of  Elementary  Mechanics  for  Colleges  and  Schools  .12mo,  1   50 
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Mechanics  of  Engineering.      Vol.     I Small  4to,  7  50 

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Maurer's  Technical  Mechanics 8vo,  4  00 

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15 


MEDICAL. 

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de  Fursac's  Manual  of  Psychiatry.      (Rosanoff  and  Collins.)..  .  .Large  12mo,  2  50 

Hammarsten's  Text-book  on  Physiological  Chemistry.     (Mandel.) 8vo,  4  00 

Jackson's  Directions  for  Laboratory  Work  in  Physiological  Chemistry.  .8vo,  1  25 

Lassar-Cohn's  Practical  Urinary  Analysis.      (Lorenz.) 12mo,  1  00 

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*  Pozzi-Escot's  Toxins  and  Venoms  and  their  Antibodies.     (Cohn.).  .  12mo,  1  00 

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Tate  and  Stone's  Foundry  Practice 12mo,  2  00 

Thurston's  Materials  of  Engineering.     In  Three  Parts 8vo,  8  00 

Part  I.       Non-metallic  Materials  of  Engineering,  see  Civil  Engineering, 
page  9. 

Part  II.     Iron  and  Steel 8vo,  3  50 

Part  III.  A  Treatise  on  Brasses,  Bronzes,  and  Other  Alloys  and  their 

Constituents 8vo,  2  50 

Ulke's  Modern  Electrolytic  Copper  Refining 8vo,  3  00 

West's  American  Foundry  Practice 12mo,  2  50 

Moulders'  Text  Book 12mo,  2  50 

16 


MINERALOGY. 

Baskerville's  Chemical  Elements.     (In  Preparation.). 

Boyd's  Map  of  Southwest  Virginia Pocket-book  form.  $2  00 

*  Browning's  Introduction  to  the  Rarer  Elements 8vo,  1  50 

Brush's  Manual  of  Determinative  Mineralogy.      (Penfield.) 8vo,  4  00 

Butler's  Pocket  Hand-book  of  Minerals 16mo,  mor.  3  00 

Chester's  Catalogue  of  Minerals 8vo,  paper,  1  00 

Cloth,  1  25 

*  Crane's  Gold  and  Silver 8vo,  5  00 

Dana's  First  Appendix  to  Dana's  New  "System  of  Mineralogy".  .Large  8vo,  1  00 
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Large  8vo, 

Manual  of  Mineralogy  and  Petrography 12mo,  2  00 

Minerals  and  How  to  Study  Them 12mo,  1  50 

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Text-book  of  Mineralogy 8vo,  4  00 

Douglas's  Untechnical  Addresses  on  Technical  Subjects 12mo,  1  00 

Eakle's  Mineral  Tables 8vo,  1  25 

Eckel's  Stone  and  Clay  Products  Used  in  Engineering.     (In  Preparation). 

Goesel's  Minerals  and  Metals:  A  Reference  Book 16mo,  mor.  3  00 

Groth's  Introduction  to  Chemical  Crystallography  (Marshall) 12mo,  1   25 

*  Hayes's  Handbook  for  Field  Geologists 16mo,  mor.  1  50 

Iddings's  Igneous  Rocks 8vo,  5  00 

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Johannsen's  Determination  of  Rock-forming  Minerals  in  Thin  Sections.  8vo, 

With  Thumb  Index  5  00 

*  Martin's  Laboratory    Guide    to    Qualitative    Analysis    with    the    Blow- 

pipe  12mo,  60 

Merrill's  Non-metallic  Minerals.  Their  Occurrence  and  Uses 8vo,  4  00 

Stones  for  Building  and  Decoration 8vo,  5  00 

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Domestic  Production 8vo.  1  00 

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*  Ries's  Clays:  Their  Occurrence,  Properties  and  Uses 8vo.  5  00 

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States 8vo.  2  50 

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Washington's  Manual  of  the  Chemical  Analysis  of  Rocks 8vo,  2  00 


MINING. 

*  Beard's  Mine  Gases  and  Explosions Large  12mo,  3  00 

Boyd's  Map  of  Southwest  Virginia Pocket-book  form,'  2  00 

*  Crane's  Gold  and  Silver gvo  5  QQ 

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*  8vo,  mor.  5  00 

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Ihlseng's  Manual  of  Mining 8vo,  5  00 

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Peele's  Compressed  Air  Plant  for  Mines 8vo.  3  00 

Riemer's  Shaft  Sinking  Under  Difficult  Conditions.      (Corning  and  Peele).8vo.  3  00 

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Wilson's  Hydraulic  and  Placer  Mining.     2d  edition   rewritten 12mo[  2  50 

Treatise  on  Practical  and  Theoretical  Mine  Ventilation 12mo.'  1  25 

17 


SANITARY   SCIENCE. 

Association  of  State  and  National  Food  and  Dairy  Departments,  Hartford 

Meeting,  1906 8vo,  $3  00 

Jamestown  Meeting,  1907 8vo,  3  00 

*  Bashore's  Outlines  of  Practical  Sanitation 12mo,  1  25 

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*  Merriman's  Elements  of  Sanitary  Enigneering 8vo,  2  00 

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Ferrel's  Popular  Treatise  on  the  Winds 8vo,  4  00 

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Gannett's  Statistical  .Abstract  of  the  World 24mo,  75 

Haines's  American  Railway  Management 12mo,  2  50 

Hanausek's  The  Microscopy  of  Technical  Products.     (Win ton) 8vo,  5  00 

18 


Jacobs's  Betterment    Briefs.      A    Collection    of    Published    Papers    on    Or- 
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Metcalfe's  Cost  of  Manufactures,  and  the  Administration  of  Workshops.. 8 vo,  5  00 

Putnam's  Nautical  Charts 8vo,  2  Of) 

Ricketts's  History  of  Rensselaer  Polytechnic  Institute  1824-1894. 

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Standage's  Decoration  of  Wood,  Glass,  Metal,  etc 12mo,  2  00 

Thome's  Structural  and  Physiological  Botany.      (Bennett) 16mo,  2   25 

Westermaier's  Compendium  of  General  Botany.      (Schneider) 8vo,  2  00 

Winslow's  Elements  of  Applied  Microscopy 12mo,  1  50 


HEBREW   AND    CHALDEE    TEXT-BOOOKS. 

Gesenius's  Hebrew  and  Chaldee  Lexicon  to  the  Old  Testament  Scriptures. 

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OF    THE 

UNIVERSITY 

OF 


YC   12780 


r 

3 


196478 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 
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28J"I 


'53KW 


Entropy 

1.64     1.56    1.58     1.60    1.62    1.64    1.66     1.68     1.70     1.72     1.74     1.76    1.78    1.80     1.82     1.84 


iving  Heat  Contents,  Volumes 
Quality  or  Superheat. 


.52    1.54      l.fifi      1.58      l.RO      1  T.2      1  PA     1  fifi      1  FA      1  70      1.72      1.74      1  7fi      1.78      1.80      1.82     1.84 


